In fortress mode, a dwarf who has no skills above dabbling level (no skills at Novice or better, military and social skills excluded) has no profession, and is listed as a "peasant" on the screen listing all creatures on the game map ( ) and the status screen ( ). By default they are shown as teal.
Peasants commonly arrive with new immigrants. All children (even children of nobles) become peasants when they reach adulthood. If you have "All Dwarves Harvest" set on the rders menu, it is possible that when a child becomes an adult, they will already have advanced skills (even legendary) as a Planter (see harvesting). However, they will still be a peasant until any one skill granting job is done. Then their title will change to reflect their highest skill (planting).
Peasants have default labors enabled when they arrive or become adults. By turning on different labors*, peasants can accomplish any task (at an untrained level of competence) and eventually be trained in any skill, or used as-is as an unskilled, no-attribute hauler. They are often chosen to be trained for military purposes, or dragooned into the Fortress guard to make up the numbers.
(* This can be done a variety of ways, "iew, references, abor" being one of the more common.)
Unlike other civilians, when a hostile creature comes in range of a peasant, they will attack it head on rather than running away, giving more valuable dwarves time to escape and holding the enemy off until the military arrives. They can often kill kobold thieves and goblin snatchers without the military ever having to step in, but can be severely wounded and often killed if encountered by a larger force.
Peasants are also invaluable as sacrificial lambs. They are largely useless and, unless applied to a practice, will eat and drink away the other dwarves' rations while contributing nothing to society themselves. It it thus a good idea to draft them to jobs that will likely result in the death of the dwarf. A good example of this would be experiments involving magma, heavily flowing water, or just about anything deadly. Just make sure they don't have a lot of friends (which may be the case if they are left to idle for extended periods of time), or you may end up with a tantrum spiral on your hands.