Utility is something that makes a job useful beyond its basic abilities. Usually these are some form of party buffs, but they can also be other party support skills.

For example: BRD is a job with amazing utility. It offers:
--A passive 2% crit buff with its songs
--A party buff on Direct Hit rate in the form of Battle Voice
--MP refresh for healers/casters (Refresh)
--TP Refresh for tanks/melee/physical ranged (Tactician)
--Utilties in the form of additional cooldowns (Nature's Minne & Palisade)
--Troubadour (offers damage reduction based on the song you use the skill in)

Other jobs with a lot of utility are: DRG, NIN, and MCH. AST has massive utility in its card system.
A few other jobs also have small bits of utility: SMN, RDM, SCH, PLD and WAR.
Some jobs have little to no utility: DRK (only has TBN), SAM, BLM, and WHM.