Answer:
One definition given in Botany, is that a rain forest is a forest containing a wide variety of tree species.
It does not require a lot of rain, though there may well be. Often there are several distinct levels of the vegetation. A Canopy layer, a mid-storey layer, and a ground layer. Completed perhaps with vines, ferns, and ground cover plants.
The monoculture forests of Washington State, for example, would not qualify as rainforest.