When you swim the backstroke, you lie on your back in the water and move your arms up and back over your head while you kick your feet. It's hard to see where you're going when you do the backstroke.
If you swim competitively on a swim team, the backstroke is one of the four official strokes for racing. Some swimmers prefer the backstroke because it's easier to breathe than when you swim face-down, though it's harder to tell how close you are to the pool wall. You can also use backstroke as a verb: "I'll just backstroke over to the shallow end and say hi to my friend."