Fox-trotting

Fox-trotting is a simple movement technique that can increase many character's dashing speed. It uses the speed of most character's initial startup dash, which is more often than not faster than their speed at full sprint, to create a faster continuous run speed. Characters most notably affected are Fox, Captain Falcon, Roy, and Marth.

To perform a Fox-trot, dash forward, return the analog stick to neutral, and dash forward again. Repeat as desired. The timing is different for every character but fairly easy to pick up on. Fox-trotting can also be performed by jump-canceling a dash into a wavedash and then restarting the run animation, and by dash-canceling a run into another dash.

In Brawl, there is a small chance that one will trip when they dash, thus attempting to Fox-Trot will increase the odds of tripping, making it a much greater risk.

Dash Sliding, a variant of Fox-trotting, is described as a constant state of dashing. It is done by mashing the control stick in an direction, and then returning it to neutral, then repeating, similar to a Foxtrot. It differs from a foxtrot in that when doing a Foxtrot, a dash-dance was needed to change directions. In a Dash Slide, it is possible to shield cancel out of it. Also, since most characters hunch over in the animation, you are a smaller target for an added bonus. This can be used as a mindgame, or as a speed advantage over your opponent.

The term was coined by Clan, Hoboking, and Legend of Brawlcentral. The whole thread is here: [1]