To participate in a tournament players have to sign up and pay a buy-in fee and house fee prior to playing. The house fee is usually 10% (or lower) of the buy-in.
For the fixed tournament fee, each player receives the same number of tournament chips. The blinds and antes at every table in play increase periodically at pre-determined intervals. This is to ensure that the tournament reaches a conclusion.
Prizes are typically awarded to the top percentage of surviving players from the field - usually between 10 and 20% of the field. The pay-out structure of any tournament can be reviewed in the lobby once you are seated and playing. To do this, click on the lobby, find the tournament you are in, and then click on 'Prize Pool'.
In 'freezeout tournaments' players can't purchase any additional chips beyond the starting stack. However, in rebuy tournaments players can buy more chips if they lose their starting chips, and also often 'top-up' at the end of the set rebuy period.
Very simply, Cash Games are games where the chips on the table represent their actual cash value. The blinds and/or antes stay at exactly the same level, and you can re-buy at any point if you drop below a certain number of chips. You can also 'cash out' at any point in Cash Games, whereas tournaments must be played until you run out of chips or win the game.