In addition to TAR86's good explanation I add an example to visualise the different molecular orbitals.
A few general remarks up front though.
Quite a few textbooks (especially in organic chemistry) use the term quantum mechanical calculations (or variations thereof) in a (somewhat) sloppy fashion. They offer (generalised) phenomenological explanations based on such calculations. This is in principle good, as we are moving away from a purely Lewis-structure based understanding of bonding and man-made concepts as ring/ torsional/ angle strain, ±I/M, resonance, etc. (the list is almost infinite) towards a more generalised, complete, overarching understanding, but it can also lead to ambiguity. Sometimes (read: often) books forget to mention the limitations of such explanations and the justification of such models is left as an exercise of critical thinking to the reader.
As the average chemist progresses from basic to advanced understanding of bonding it can get confusing since some books use similar terms for different things. One of the common things is arguing with localised orbital schemes, predefined hybrid orbitals and the likes, which allow little to no flexibility. While these arguments are also deeply rooted in theoretical chemistry, i.e. Valence Bond theory, the source of the computation is most times in terms of Molecular Orbital theory. Rather than performing the extensive (and quantitative) calculations applying the former, the more common Molecular Orbital approaches (Linear combination of atomic orbitals to form molecular orbitals; or LCAO=MO) are used, such as Hartree-Fock, post-HF and Density Functional Approximations. The latter are so well developed that it won't be long that we can run simple calculations on the fly on our phones (The future is here ...).
When you start learning quantum chemical calculations you might be confused at first, because a lot of such tempting model explanations don't seem to fit any more.
Orbitals. First and probably most important is to realise that the shapes we recognise as orbital depictions are not real in any sense. These are visualisations of mathematical functions at a certain cut-off value. This is necessary as a wave function (in principle) only vanishes at infinity. In this sense, orbitals obviously always span the entire molecule. But this is in general not the reason why we say molecular orbitals span the entire molecule; this is a general feature of Molecular Orbital theory (as opposed to Valence Bond theory).
Molecular Orbitals Interpretation. I have used DF-BP86/def2-SVP to run a quick geometry optimisation of staggered ethane with Gaussian09. The approach to obtain molecular orbitals on this level of theory is similar to Hartree-Fock as in that it uses one Slater-Determinant (not a product of wave functions!) as the trial function only.
The results are thus similar to the canonical orbitals you would obtain from a HF solution. (For all intents and purposes in this example we regard them as equal.)
The general feature of this approach is that all atomic orbitals contribute in some fashion to the set of molecular orbitals. The coefficients to the atomic orbitals are optimised in a way that the expectation value of the energy of the trial function is minimal. Therefore in many cases they look like the following picture.

In the graphic above, the orange/blue orbitals are occupied and the red/yellow ones are virtual; core orbitals omitted. Because of symmetry we have some degenerate orbitals in the mix. Strictly speaking only the occupied orbitals are actual solutions to the pseudo-Eigenvalue problem, but we can use these to generate virtual (high energy) solutions, too. While these orbitals offer a general understanding, and often reproduce ionisation potentials and electron affinities, it is difficult to interpret them with the conventional understanding (of Lewis structures) that the organic chemists love so much.
Localised Orbitals and the Valence Bond Interpretation. There are numerous localisation schemes for canonical orbitals out there. Different approaches use different criteria. A common approach is to use linear combinations of the canonical orbitals to produce a different set of molecular orbitals with a compacter spatial extend, more of the electron density is contained in a smaller volume. The general aim is to produce orbitals which represent bonds where we expect them. Through this approach we loose some of the properties, especially those which are energy related.
One of these approaches in Natural Bond Orbital theory, which aims to provide a description as close as possible to Lewis structures. I have performed such a localisation with NBO 6.0 and it resulted in a much more familiar orbital picture:

(I have pulled the σ(*)-C-C bond orbital below the sp3-C-H bonds. In the output, below, these are between the triads.)
One of the main features of such localised orbitals are fractional occupation numbers. These then allow some more interpretations like the ones you have encountered, i.e. interactions between (mostly) occupied and (mostly) unoccupied orbitals. In this scheme your picture results in the following representation:

The above picture could be calculated quantitatively with a valence bond orbital approach, which uses hybrid orbitals and molecular conformations as an input. This usually needs considerably more calculation time as it is in theory already more extensive and more expansive. However, qualitatively it would probably reproduce the above picture (just more accurately), and often offers only for extraordinary bonding situations considerably more insight. As such, MO theory is complementary to VB theory; at their respective complete treatments they are equal.
Addendum. The calculation was run with Gaussian09 rev. D01 with tight convergence criteria and loose symmetry recognition. Convergence into a local minimum has not been checked. The optimised structure is in Cartesian coordinates in angstrom:
scf (DF-BP86/def2SVP) done: -79.763139
C -0.111323 0.000000 -1.496408
H -0.111323 1.032093 -1.906398
H 0.782495 -0.516047 -1.906398
H -1.005142 -0.516046 -1.906398
C -0.111323 0.000000 0.035289
H -1.005142 0.516047 0.445279
H -0.111324 -1.032093 0.445279
H 0.782496 0.516046 0.445279
The displayed canonical orbitals have the following contributions (Display threshold 5%):
Alpha occ 3 OE=-0.672 is C5-s=0.34 C1-s=0.34
Alpha occ 4 OE=-0.544 is C1-s=0.19 C5-s=0.19 H2-s=0.07 H7-s=0.07 H4-s=0.07 H8-s=0.07
H3-s=0.07 H6-s=0.07 C5-p=0.07 C1-p=0.07
Alpha occ 5 OE=-0.384 is C1-p=0.30 C5-p=0.30 H7-s=0.13 H2-s=0.13
Alpha occ 6 OE=-0.384 is C1-p=0.30 C5-p=0.30 H3-s=0.10 H4-s=0.10 H8-s=0.10 H6-s=0.10
Alpha occ 7 OE=-0.329 is C1-p=0.40 C5-p=0.40
Alpha occ 8 OE=-0.298 is C5-p=0.21 C1-p=0.21 H7-s=0.19 H2-s=0.19
Alpha occ 9 OE=-0.298 is C1-p=0.21 C5-p=0.21 H6-s=0.14 H4-s=0.14 H8-s=0.14 H3-s=0.14
Alpha vir 10 OE=0.048 is C5-s=-0.26 C1-s=-0.26 H7-s=0.24 H2-s=0.24 H3-s=0.24
H8-s=0.24 H6-s=0.24 H4-s=0.24
Alpha vir 11 OE=0.090 is H2-s=0.22 H7-s=0.22 H3-s=0.22 H4-s=0.22 H8-s=0.22
H6-s=0.22 C1-s=-0.22 C5-s=-0.22
Alpha vir 12 OE=0.100 is H3-s=0.24 H8-s=0.24 H4-s=0.24 H6-s=0.24
Alpha vir 13 OE=0.100 is H7-s=0.32 H2-s=0.32 H6-s=0.08 H8-s=0.08 H4-s=0.08 H3-s=0.08
Alpha vir 14 OE=0.134 is H8-s=0.22 H6-s=0.22 H4-s=0.22 H3-s=0.22 C5-p=0.05 C1-p=0.05
Alpha vir 15 OE=0.134 is H2-s=0.29 H7-s=0.29 H3-s=0.07 H6-s=0.07 H4-s=0.07 H8-s=0.07
C1-p=0.05 C5-p=0.05
Alpha vir 16 OE=0.195 is C5-p=0.43 C1-p=0.43
The displayed NBO have the following contributions (cleaned):
(Occupancy) Bond orbital / Coefficients / Hybrids
------------------ Lewis ------------------------------------------------------
3. (1.98857) BD ( 1) C 1- H 2
( 61.06%) 0.7814* C 1 s( 23.30%)p 3.29( 76.67%)d 0.00( 0.04%)
( 38.94%) 0.6240* H 2 s( 99.91%)p 0.00( 0.09%)
4. (1.98858) BD ( 1) C 1- H 3
( 61.06%) 0.7814* C 1 s( 23.30%)p 3.29( 76.66%)d 0.00( 0.04%)
( 38.94%) 0.6240* H 3 s( 99.92%)p 0.00( 0.08%)
5. (1.98858) BD ( 1) C 1- H 4
( 61.06%) 0.7814* C 1 s( 23.30%)p 3.29( 76.66%)d 0.00( 0.04%)
( 38.94%) 0.6240* H 4 s( 99.92%)p 0.00( 0.08%)
6. (1.99640) BD ( 1) C 1- C 5
( 50.00%) 0.7071* C 1 s( 30.13%)p 2.32( 69.83%)d 0.00( 0.04%)
( 50.00%) 0.7071* C 5 s( 30.13%)p 2.32( 69.83%)d 0.00( 0.04%)
7. (1.98858) BD ( 1) C 5- H 6
( 61.06%) 0.7814* C 5 s( 23.30%)p 3.29( 76.66%)d 0.00( 0.04%)
( 38.94%) 0.6240* H 6 s( 99.92%)p 0.00( 0.08%)
8. (1.98857) BD ( 1) C 5- H 7
( 61.06%) 0.7814* C 5 s( 23.30%)p 3.29( 76.67%)d 0.00( 0.04%)
( 38.94%) 0.6240* H 7 s( 99.91%)p 0.00( 0.09%)
9. (1.98858) BD ( 1) C 5- H 8
( 61.06%) 0.7814* C 5 s( 23.30%)p 3.29( 76.66%)d 0.00( 0.04%)
( 38.94%) 0.6240* H 8 s( 99.92%)p 0.00( 0.08%)
---------------- non-Lewis ----------------------------------------------------
10. (0.00902) BD*( 1) C 1- H 2
( 38.94%) 0.6240* C 1 s( 23.30%)p 3.29( 76.67%)d 0.00( 0.04%)
( 61.06%) -0.7814* H 2 s( 99.91%)p 0.00( 0.09%)
11. (0.00902) BD*( 1) C 1- H 3
( 38.94%) 0.6240* C 1 s( 23.30%)p 3.29( 76.66%)d 0.00( 0.04%)
( 61.06%) -0.7814* H 3 s( 99.92%)p 0.00( 0.08%)
12. (0.00902) BD*( 1) C 1- H 4
( 38.94%) 0.6240* C 1 s( 23.30%)p 3.29( 76.66%)d 0.00( 0.04%)
( 61.06%) -0.7814* H 4 s( 99.92%)p 0.00( 0.08%)
13. (0.00098) BD*( 1) C 1- C 5
( 50.00%) 0.7071* C 1 s( 30.13%)p 2.32( 69.83%)d 0.00( 0.04%)
( 50.00%) -0.7071* C 5 s( 30.13%)p 2.32( 69.83%)d 0.00( 0.04%)
14. (0.00902) BD*( 1) C 5- H 6
( 38.94%) 0.6240* C 5 s( 23.30%)p 3.29( 76.66%)d 0.00( 0.04%)
( 61.06%) -0.7814* H 6 s( 99.92%)p 0.00( 0.08%)
15. (0.00902) BD*( 1) C 5- H 7
( 38.94%) 0.6240* C 5 s( 23.30%)p 3.29( 76.67%)d 0.00( 0.04%)
( 61.06%) -0.7814* H 7 s( 99.91%)p 0.00( 0.09%)
16. (0.00902) BD*( 1) C 5- H 8
( 38.94%) 0.6240* C 5 s( 23.30%)p 3.29( 76.66%)d 0.00( 0.04%)
( 61.06%) -0.7814* H 8 s( 99.92%)p 0.00( 0.08%)