The official answer: it is extremely important to warm up before any physical activity, especially gymnastics.
The real answer: it depends on how old you are and what level you're at. If a 20-year-old is working on full-twisting double layouts and he doesn't warm up first, he will very likely get severely injured. If a 9-year-old is working on her cartwheels and doesn't warm up, she'll probably be fine.
As far as what a warm up should consist of, preferences vary HUGELY, but a general rule of thumb is that it should do two things:
1) Loosen up any muscles that may be tight from lack of use within the last hour or two.
2) Get the blood pumping, get the adrenaline up, and get the gymnast ready to go.