Gymnastics have sections called events:
Womens Gymnastics Have Different Events Than Mens Gymnastics
The Events listed above are listed in the Olympic order, which means you compete (in womens) vault first, then uneven bars, balance beam, then lastly floor exercise. Competitions also add up the score of all four events (women) or the six events (men). This category is called All Around.
Events are graded out of 10 in USAIGC competitons. Meaning that All Around is thus scored out of a 40. The scores can go as far as to the hundredth place. For example, you can score an 8.32.
Common deductions are falls (which is roughly 0.5) and bent knees/arms (which is 0.2). Another common deduction is a missing element; meaning you forgot a certain move (which is a 0.8)