Clearly, this issue has been touched on here and here. However, I would like to raise a new point on the issue.

I have always thought that stabilisation of the $\ce {C=C}$ $\pi$ bond via hyperconjugation is through an interaction between a $\ce {C-C}$ or $\ce {C-H}$ $\sigma$ MO and the $\pi^*$ MO. This is also the explanation presented by orthocresol and Philipp in the posts linked above. However, the explanation given by Fleming (2009) is somewhat different as can be seen from the diagram below, taken from p. 74

There seems to be an internal contradiction in the text. On the previous page, Fleming does mention about the interaction between the $\sigma$ MO and the $\pi^*$ MO yet the diagram shows an interaction between a $\sigma$ MO and the $\pi$ MO. Not sure if it's a misinterpretation on my part...

On p. 73, he wrote:

One factor is the hyperconjugative stabilisation of the $\ce {C=C}$ $\pi$ bond by the alkyl groups. Fig. 2.11 shows the interaction of the orbitals of a $\sigma$ bond with the orbitals of a $\pi$ bond, which is similar to the interaction of two $\pi$ bonds in butadiene (Fig. 1.32). Although the $\sigma$-bonding orbital and the $\pi^*$-antibonding orbital are further apart than $\psi_2$ and $\psi_3^*$ in butadiene, they are just close enough to mix in a bonding sense effectively to lower the energies of $\psi_1$ and $\psi_2$ in Fig. 2.11, making the drop in energy $\ce {E1}$ a little greater than the rise inenergy $\ce {E2}$.

Reference

Fleming, I. Molecular Orbitals and Organic Chemical Reactions. John Wiley & Sons, Ltd. United Kingdom, 2009.