Electrons always jump from HOMO to LUMO. The ordering of MOs usually goes like this, in order of increasing energy: sigma bonding, pi bonding, pi anti-bonding, sigma anti-bonding. This is because sigma bonding orbitals are stabilized with respect to pi bonding orbitals because sigma bonding orbitals have end-on-end overlap. Therefore, since sigma anti-bonding orbital is de-stabilized as much as sigma bonding is stabilized, it's very high up in energy. On the other hand, pi bonding is less stabilized with respect to sigma bonding and therefore pi anti-bonding is less destabilized relative to sigma anti-bonding.
Just take a look of MO diagrams for various molecules. HOMO is generally a pi bonding orbital and LUMO is generally a pi anti-bonding orbital.
Unfortunately, we teach basic rules in organic chemistry because many students don't have the MO background to understand molecular orbital theory. Very few people do. So we teach "rules," namely that UV is good for distinguishing conjugated organic compounds and each conjugated compound will exhibit a distinct shift in the UV spectrum. For example, benzene's characteristic shift is analyzed at 254 nm.
So the theory behind that is that increased conjugation results in a lowering of the HOMO-LUMO gap and thus lowering in the energy required to excite the electrons. A lowering of delta E directly results in a so-called redshift, or shift to higher wavelengths.