Character sheets are what allow you to get the basics of your character down on paper. The most basic kinds will just ask for a few things, and look something like this:

Name:
Age:
Appearance:
Personality:
History:


And then some will go into more depth, like this:

Name:
Race/Species:
Age:
Height:
Hair:
Eyes:
Clothes:
Appearance:
Personality:
History:
Weapons:
Skills:
Paraphernalia:


And so on and so forth, with each GM modifying categories to fit their game - for example if they were playing as horses instead of people, they might ask for mane, tail, coat, instead of hair and clothes.

For the dice-based games, the sheets will have slots for things like:

Body:
Dexterity:
Wisdom:
Mind:
Personality:


with each slot being assigned a certain number of points. You are given a number of points (say 10), and each category is given a minimum and maximum number of points (say 1 to 5) to limit your maximum capability and to provide a scale for comparison. The total is then divided among the categories, like so:

Body: 2
Dexterity: 1
Wisdom: 3
Mind: 3
Personality: 1


Or something like that. Different roleplaying systems (ie, Dungeons & Dragons 4th Edition, World of Darkness, GURPS) will use different variations on this theme with varying levels of complexity.

The point behind character sheets is to allow other people to understand what your character is capable of.