Fortify was mainly used defensively to prevent towers from taking damage and clearing creeps faster than normally. However it was also a very effective method to punish tower divers or quickly do damage to foes that got caught by pulls and taunts like Rocket Grab and Puncturing Taunt.
While fortified, a turret grants you assists and kills when it last-hits or assists in killing an enemy champion as if you were dealing the damage, and not the turret. This does not, however, apply to minion kills.
After the V188.8.131.52 patch update, players who achieved summoner level 4 reported having the message that they have learned Fortify. This tooltip may have been left out during the patch's installation.