Learning to draw quickly means learning to use a single mark with economy and using that mark to capture an impression of the subject.
Capturing a subject in motion—a moving person or animal, for instance—comes down to focusing not on the details of the subject, but the essence of a pose or gesture. In drawing quickly, you convey the personality of the subject, capturing as much with one line as quickly as possible.
This is not a style of drawing where you’ll want to get hung up on the details. Work down to the details from the initial impression or gesture.