Most digital cameras have a continuous shooting mode, where shots are taken one after the other in rapid succession.
When taking shots, there is often a short delay between when you press your finger on the button, and when the picture is actually taken. This delay may mean your subject has finished their action (eg blowing out candles on a cake) and you have missed the magic moment.
With Continuous Shooting you can take a sequence of shots and keep just the right one. Continuous Shooting also increases you chances of capturing a candid moment.
Where else can this be useful? Any shots of children or group shots will benefit from continuous mode.