People use the whip analogy and it's a good one. But the term I see most often in kinetic linking.
Getting snap into your punches is about getting the proper transfer of power from your legs, through your hips, and out through your arms. When it's done properly, your arms almost move on their own - snapping out like the end of whip.
A simple tool to help learn that feeling is to throw punches with your arms handing loosely at your side. Get into your stance but instead of holding your arm in guard, let hang them loosely by your sides, like strings of spaghetti. Now throw a punch with your legs, hips and core.
If you're getting proper power transfer, your arm should start to swing just from the momentum your lower body is generating. That's the core principle in generating snap. If you can get your arms to swing out and then pull them back with just the power from your legs and hips then you can move on to practicing with your hands up in guard.
The difference is that you must be loose enough to let your arms snap out with your hips power but controlled enough to not lose your guard. But one step at a time. Proper power transference is the key.
EDIT: This is the same regardless of what punch you're throwing - jabs, crosses, hooks, overhands, uppercuts, etc. The only difference (well, not the only difference) is what path the arm travels. Combine that with information from a thread that sinister made a while back about how to properly form a fist and what knuckles to land with and you have your basics for punching technique.