Your 3 stations let you borrow one route at the end of the turn. On your turn, pay the cards needed (one card for the first station, 2 identical ones for the second, etc.) and place a station on a city that the borrowed route connects to. You may borrow one route per station. Also, every station you don't build gives 4 points.
Stations are only officially used in Europe, where they are vital due to the shape and distribution of the map, however they can easily be house-ruled onto almost any map to ease congestion or to combat blocking.
