Why does the reduction of NAD+ to NADH change the absorbance so much, and cause fluorescence?
Essentially NADH has an additional pair of electrons. These additional electrons which are oftein drawn as a lone pair of electrons alters the molecule in a similar way to the way in which many pH indicators change upon protonation.

Here are diagrams of the reduced and oxidized forms of NADH / NAD+



A typical indicator when protonated appears to have a colour, however upon deprotonation the indicator loses a hydrogen and gains a lone pair of electrons now appearing to have a different colour. The addition of the lone pair of electrons actually lowers the transition energy between the pi bonding and the pi anti-bonding states. 

For example for methyl red it can be predicted that the unprotonated form has a HOMO/LUMO gap of 2.175 eV (according to extended Huckel calculations). For the protonated form of methyl red has a HOMO/LUMO gap of 3.275 eV.

This lowered energy correlates with a decreased absorbance energy, ultimately reflecting a higher energy wave of light (Frequency of Blue > Red). NADH's absorbance wavelength his greater than NAD+'s absorbance wavelength, because NADH is absorbing lower energy light. This, like pH indicators, is due to the lone pair lowering pi and pi anti-bonding energy state differences.