Vikings are one of several jobs provided by the Water Crystal, and therefore are in the third tier of jobs. They are alluded to a bit earlier though, as a gang of vikings have a cove on the Floating Continent. After Final Fantasy III Vikings make scare appearances throughout the series.
If the Warrior is considered a slower physical attacker than the Thief, then the Viking is a slower physical attacker than the Warrior. Not only is their speed unimpressive, but they wield hammers and axes, the heavier weapon types. As a result, they can be a bit unwieldy to use, relying more on singular strong hits rather than a flurry of hits like Warrior or Thief. On the flipside, their extremely high vitality makes them the perfect class to level up in if you want to increase a character's HP.
The 3D remake retools the Viking through some stat changes and a new command. In regards to stats, the Viking loses some of that vitality in favor of strength, boasting one of the highest natural attack stats at max level, among other changes. But it's the command that greatly changes the Viking, giving them a defined role and a clear role to play.
The Provoke ability causes the Viking to draw the ire of nearby enemies. This accomplishes two things: First, any single target physical attacks from affected enemies will be targeted at the Viking (a naturally tanky unit) and second, it lowers te defense of enemies it effects. These combined means that the Viking not only takes the heat off of the rest of the party but makes it easier for them to take down enemies. Sweetening the pot even further is that, compared to some other job abilities, the Viking's Provoke starts at somewhat under 50% and reaches "near-guarenteed" levels of effectiveness at max job level.
This had led to a strat that even the strategy guides acknowledge: Parking the viking in the back row, putting shields in both hands and simply drawing fire away from everyone else.