In truth, no-one can say for certain, but there are a number of theories. Some believe that since poker was often played on riverboats, cheaters who were caught dealing themselves an extra card would be thrown into the river. Others say this is not true and the term river instead comes from the french word river.
The river is the last of the community cards dealt in a game, both in poker tournaments and cash games. It's also known as fifth street, as it's the fifth and final of the five community cards. Most importantly, the river often makes or breaks a hand and decides the outcome of a showdown.