First strike lets your unit strike frist (do'h

) having the chance to deal some damage while the enemy can not retaliate. However, if and how much damage your unit will do depends on the relative strenght of the fighting units.
So:
Giving first strike to a unit that has very low odds, will not help you a lot, because while your unit will strike first, it's chances to actually do some damage with that strike are very low.
However, if you give First strike to a unit that already has high odds of winning, the first strikes will most likely be successful and deal lots of damage to a enemy, so your unit is likely to take less damage in the fight.
This might be i.e. usefull when defending against siege - by doing damage via first strike (or at least canceling the attackers first strikes) you reduce the number of combat rounds and hence the collateral damage yousr stack will take.
This makes first stirke often a good defensive promotion, as you are expecting the defender to have some advantage (good odds) and you want the defender to take as little damage as possible, so he can defend multiple times.
first strike promotions might have some use on attacks as well, but generally when attacking you rather want to give promotions increasing the odds first (like CR, or Cover/Shock), as first strikes at low odds are not very effective.