In molecular orbitals diagram, sigma ($\sigma$) and pi ($\pi$) symbols are used. What do these symbols really mean?
These symbols are for bonding orbitals. A covalent bond is formed when two orbitals in different atoms hybridize. $\sigma$ and $\pi$ refer to two different configurations in which this can happen.
In a $\sigma$ bond, two $s$ orbitals or two $p$ orbitals oriented towards each other join into one orbital, with the electron density concentrated between the two atoms.
In a $\pi$ bond, two $p$ orbitals oriented perpendicular to the bond axis merge, and, in the resulting orbital, electron density is concentrated above and below the bond axis.