[Winga]

Using MO theory to describe it, the pi & pi* orbitals from each c=c bond combine to form 4 new MOs.

Just neglect the 2 new MOs (pi3 & pi4) in highest energy (formed from 2 pi* orbitals), how can we know the conjugated dienes are more stable than simple dienes from MO diagram?

One pair electrons are occupied in pi1 (bonding) orbital and another pair are occupied in pi2 (antibonding) orbital.
The extra stability effect seems to be cancelled out and its overall energy seems unchanged compare with the original pi orbitals.

(At this moment, just concern about the MOs, no need to concern about the extent of electrons dispersion)

[movies]

It's hard to tell from just looking at p-orbitals, but it turns out the pi1 is lowered in energy more than pi2 is increased in energy.  This is because the coefficients of the orbitals is different between pi1 and pi2 such that in pi1 there is a large coefficient on carbon atoms 2 and 3 (and thus a large overlap between the two since they are in phase).  In pi2 the coefficient on carbons 1 and 4 is larger than the coefficient on carbons 2 and 3 so that the anti-bonding interaction is diminished.