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When a bet is made, and you're offered "seven to one" (usually written "7:1"), this means that the other person will pay you 7 if you win, and you will pay him 1 if you lose. 7 what or 1 what? Could be dollars, could be euros, could be cookies. Could be anything! The point is that he will pay you seven times as much if you win as you have to pay him if you lose.
So if someone offers you 7:1 on a race horse, and you take the deal and bet $20, he will pay you $140 if you win and you will pay him $20 if you lose. As a sidenote, if it's a bookmaker you're dealing with you will usually give him your $20 before the race, and he will then pay you $140 plus your $20 back after the race, i.e. $160. So if you think your horse is more likely to win than the odds you get, you should take the bet.
And if someone offers you 6:1 after the river card in Texas Hold'em, and you think you have better odds than that to win the pot, you should call. Of course, it's difficult to know if your hand is the better than your opponent's, but you should at least have some idea of how likely your hand is to be best, but it's still a matter of judgement. To avoid having to discuss judgement calls, let's look at a situation where you can be certain:
You're on the turn in Texas Hold'em, and you're holding Q♥ 9♥ in last position.
The board is A♥ K♥ 7♠ 4♠
The player before you bets. He's a tight poker player, and you know he's unlikely to bet without at least a pair of kings, and likely a pair of aces, here. Your only chance of winning this pot is if the last card is a third heart, giving you a flush. There are nine cards that you have not seen out of 46 in the deck (counting from the turn, not the flop) that will give you this flush, so you have about a 9/46 chance to hit on the river. Another way of putting this is that there are 9 cards that will make you win, and 46-9 = 37 cards that will make you lose. The odds are therefore 37 to 9, or just about 4:1. If there is more than four times as much in the pot as it costs you to call, you should continue, since you have a profitable situation!
To give another example: You have T♠ 9♠ and the board on the turn is 9♥ 8♦ 8♠ 7♣. You believe that your opponent is holding K-K or A-A. To determine your odds, we have to first figure out how many cards will make you a winner:
A jack will give you a jack-high straight, so the four remaining jacks are good for you (4). Furthermore, any of the four remaining sixes will give you a ten-high straight, so they are good as well (4). A ten would give you two pair, but won't help if he has an overpair since he would have a bigger two pair, but a 9 would give you a full house (2).
4+4+2 = 10, and 44-10 = 34 will mean that we lose. Our odds to win or split are 34:10 against, in other words, or 3.4:1. If the pot is $100, and your opponent bets $40, the pot odds will be 3.5:1 (140/40:1) which is enough to show a profit from calling.

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