A descriptor categorizes a spell in some way. Spells can have more than one descriptor.
Descriptors have no game effect by themselves and may simply be descriptive of a spell's effect (e.g. "magical armor"). But, many descriptors indicate an effect relevant to creatures attempting to avoid the spell. Specifically, descriptors are often used as the "versus" part when a saving throw bonus applies versus something (e.g. a +1 bonus on saves vs. fear). In addition, some descriptors are associated with an immunity that applies against spells with that descriptor. As an exception, damage immunities only apply against the damage inflicted of that type, not to the spell overall. (This exception is somewhat necessary, as damage immunities tend to be less than 100%.)
The descriptor-based immunity sometimes does not work as expected. When the descriptor does not match the actual effect of the spell (e.g. Tasha's hideous laughter), it may happen that immunity actually causes the save to be failed without being rolled. In addition, the "death" descriptor is unreliable as far as making a target immune to the spell. (In both cases, the general descriptor mechanism used by BioWare in spell scripts is inadequate, which requires special processing in each script to function as expected. This special processing is rarer than one might want.)
The descriptors typically relevant to spell saving throws are the following.