Fear makes you lose a couple turns at the beginning of a battle, at least if you don't resist the effect. Not sure exactly how many turns you lose. If a unit is affected by Fear, it will gain the 'Afraid' status effect, and each time its turn comes up while still under the effect of Fear, you'll see 'Afraid' show up over the unit. '-Afraid' means that that was the last turn in which your unit was affected by Fear.
It might have some other effects, but that is the one I know of.
