A flick is a quick, short movement, usually coming from the wrist or hand. There used to be a "Flick a Bic" cigarette ad: cigarettes are awful, but starting a lighter is a classic flick.
The most common flick is probably turning a switch on or off — people flick switches, like light switches. Flicking is also used when describing golfers and basketball players. A fast, sharp golf shot could be called a flick. A quick basketball shot — like tipping the ball in with one second left in the game — is also a flick. A flick can also be described as a quick jerk — not a jerk as in a bad person, but a tiny movement. If you're using your whole body or even your whole arm, you're not flicking.