When you strut, you walk with a proud swagger that has a little arrogance thrown in, like the prance of a running back who has just flown past the 250-pound linebackers and planted the ball in the end zone.
You can't strut and be shy about it — when you strut, you know people are watching you. The big boss in a gangster film, a model on the runway, and the rap artist whose album has just gone platinum all know how to strut. The noun form of strut has a little less flash and refers to a vertical or horizontal support that holds something up, like the long steel bars holding up a building.