The Fox-trot is a simple movement technique that many characters can do to increase their ground 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 Cancelling your dash into a wavedash and then restarting the run animation, and by Dash Cancelling your run into another dash.