Damage Over Time (DoT) is a term used to describe skills or spells that continue to damage monsters even after the skill has been cast. Examples of such skills are the Witch Doctor's Grasp of the Dead and Haunt. Typically, a DoT skill is described as X% damage over Y seconds. Some skills deal both instant damage and DoT.
Damage done by DoT effects is not applied at once, but drained gradually. Technically, target will suffer a hit 10 to 30 times per second (numbers popping up every 0.5 seconds). Some DoT effects can even roll a Critical Hit, but most are simply increasing their plain tick damage proportionally to the Attack Speed, Critical Hit Chance and Critical Hit Damage. They will still be affected by the target's Armor and Resistances, if any.
Many DoT skills hit everything within the area of effect, effectiverly delivering a hit to every enemy standing in a 'pool', stopping the damage as soon as target leaves the dangerous area. Note that this damage counts as inflicted in melee.
Most DoT skills have very low Proc Coefficients, but some (like Haunt) may have higher values.
Channeled skills (like Disintegrate or Firebats) also deal damage like DoT, as long as target is caught into the beam or torrent. These skills always roll normally for the Critical Hit and fully benefit from the Attack Speed, but drain Life from the target over time just like DoT.
Unlike Diablo II, where heroes could not die from being poisoned, in Diablo III, both monsters and characters can die from any DoT effect.