What happens to rainwater that falls on land?

Well there are three reasons
it drains into rivers, streams, etc. or
 it seeps into soil and gather underground as ground-water
or
falls into high mountains and freeze and in the summer it will melt and flows into the rivers

When there is precipitation, rain water mainly goes to three places

50% Absorbed to the ground.
40% Evaporation
10% Runs off.

If there is rain on already existing bodies of waters (ie rivers)
It will just be hundred precent absorbed in to the water and combined in to the same body of water. 

When the evnviroment is in a freezing environment, the rain water will freeze, and repeat its process of absorption and evaporation again once it melts.