Float fishing is one of many techniques used to catch trout. It's primary used in rivers in and streams where there's a little current to help carry the float downstream.
The video below not only shows you how to set up a float fishing rig, but offers tips on using it effectively. Note that also though the anglers in this video are using a fly rod, the rig and technique will work with a spinning rod as well.
Why does this technique work? It's because trout are lazy! In rivers and streams they often position themselves in the water so that the current brings food directly to them. The idea behind this technique is to make your bait offering move with the current and look like a natural food source to trout lying in wait.