The blinds are forced bets posted by players to the left of the dealer button in flop-style poker games. The number of blinds is usually two, but can be one or three.
The blinds exist because Omaha and Texas hold 'em are frequently played without antes, allowing a player to fold his hand without placing a bet. The blind bets introduce a regular cost to take part in the game, thus inducing a player to enter pots in an attempt to compensate for that expense.
Generally, the "big blind" is equal to the minimum bet, and is twice as much as the "small blind". The small blind is posted by the player to the left of the dealer button while the big blind is posted by the player to the left of the person sitting in the small blind. After the cards are dealt, the player to the left of the big blind is the first to act during the first betting round.
Antes are a set amount put in the pot by every player in the game prior to cards being dealt. This amount does not count toward your bet on the first round of betting, unlike blinds. This simple method is used primarily in home games. This method also is not very common with texas hold em specifically, it's more often found in games like five-card stud or draw. Antes are also used in conjunction with blinds in the later stages of a tournament.
Based on the limit of the game, the player to the left of the dealer's button (the small blind) and the player two to the left of the button (the big blind) are required to put up mandatory bets before the cards are dealt. These blinds count toward your total investment toward the first round of betting. So if the pot isn't raised pre-flop, the small blind will only have to put in another half a bet to call. Likewise, the big blind won't have to put anything more in the pot, although the big will have the ability to raise his own blind. In an unraised pre-flop pot, this is referred to as the "option".
The amount that is put out depends on the limit. In fixed limit poker, the big blind puts up a bet equal to the small limit. The small blind puts up half that amount. So if the limit is $5/$10, the big blind is $5 and the small blind is $2.50. This is not like a no limit or pot limit poker game. In a $5/$10 no limit hold'em game, the small blind would be $5 and the big blind would be $10.