Epiphytes are plants which rely on other larger plants for physical support. Epiphytes are totally independent otherwise. They do not take anything out of their host plant that supports them. This distinguishes them from Parasitic plants, such as the Mistletoe, which i wrote a post on recently.
An Epiphyte derives it's nutrients from the air, rain, and from the debris that accumulates around it's roots. Debris comes from it's host tree ( fallen leaves etc) and also from bird droppings , insects and other things that fall out of the tree canopy, and these provide nutrients as they collect and decay. Epiphytes provide valuable habitat for Birds, insects, frogs, and many other creatures.
Some common Epihpytic plants include Orchids, different types of Ferns, Bromeliads and Cacti. The photo here is of an Orchid in the fork of an old tree in North-Western New South Wales, Australia.