The Warrior job is one of the first jobs you get in Final Fantasy III. For the first half of the game, it is the primary go-to attacker of the party, being the primary sword user and having the ability to equip shields. However, FFIII is the first game that allows characters to dual-wield without penalty so twin swords is a very viable, very lucrative strategy. Overall, the Warrior is a solid choice for a good chunk of the first half of the game, but once you get the Knight, there's no point in sticking with it.
The remake tweaks the Warrior in a few subtle ways, primarily giving it a new ability known as Advance. Its weapon pool is also expanded, allowing it to remain a reliable damage-dealer even at the end of the game.
The Advance command gives the Warrior increased attack power at the cost of lowering defense. The amount is proportional between both ends (i.e. if Advance grants you a 10% damage increase, it also slams you with a 10% damage decrease). The bonus/debuff increases over job levels, meaning that the Warrior can get stronger and stronger the more he has... as well as more and more fragile.
Partnering with a defensive class is a must. As Advance scales in terms of levels, a Warrior gets more and more fragile as they use it. A Knight or a Viking, however, can provide some protection from physical attacks, giving the Warrior more incentive to rely heavily on the move.