Vented dryers are very traditional. Dryers with this style draw in air from the room then heating it. The dryer uses that hot air to evaporate the water out of your clothes then exhausting it out side of your home. This process could be energy intensive so be sure to check you owner manual.
Ventless dryers are a newer design. Ventless dryers heat your wet clothes in an inner drum or tub. The heat then evaporates the water out of your clothes producing steam, where it flows through holes out of the inner drum. Once the steam reaches the outer drum it then condenses back to water. Once the steam converts to water it simply drains out of the unit. This process requires no outside venting, which allows for an easier installation.