There are lots of numbers associated with sports odds. I'd need to know which numbers specifically you're asking about.
The most common numbers people ask about would be the point spread, which is a form of "handicapping" the game, offering extra points to one competitor or the other, to influence bettors to place a bet for or against a team, based on how you think that team will do, with the point spread added to or subtracted from their final score.
For instance, suppose the Tampa Bay Buccaneers are scheduled to play the Kansas City Chiefs in Kansas City, and the point spread has Kansas City +3 points. This means that, whatever the final score of the game, the oddsmakers in Las Vegas are going to add 3 points to Kansas City's total, and then pay off bets based on that adjusted score. So if the game actually ended with Tampa Bay winning 21-20, anybody who bet on Kansas City wins the bet, because the adjusted score is Kansas City 23 (20 real points +3 point spread) to Tampa Bay's 21.
It should be mentioned that the Vegas point spread is not necessarily a prediction of the outcome of the game. It's actually an incentive to get the betting public to bet on one particular team, with the goal being to get the exact same amount (or, as close as possible) bet on both teams. This reduces the risk that the casinos take, since the winning bettors will be paid from the losing bettors, and the casinos get to make their money by keeping their "skim," a small percentage of the money changing hands between the two sides.
The predicted outcome of the game obviously weighs heavily on the point spread, but (using my earlier example) if everybody thinks that Tampa is going to crush Kansas City, and all the bets come in on the Tampa Bay side at the casino, then they're going to slowly raise the point spread in Kansas City's favor as the week goes along, to attract more people to bet on Kansas City...not because they've suddenly changed their mind, and think Tampa Bay's going to score more points, but just to protect themselves, in case Tampa Bay does wind up "beating the spread" and the casino has to pay off all the winners out of their own money, with fewer losing bettors kicking in any money.
Response to Additional Details:
You've given an example of bets that includes a "money line" for each of the bets shown. The first two lines are point spread bets, like I explained earlier. Tennessee is an 18.5 point underdog, and will have 18.5 points added to their final score and the winner of bets on their game will be based on that adjusted score.
The "-110" you see after the point spread is the money line for that game. This outlines how much money you'll make for winning that particular bet. When you see a negative number like that, it means that the bookmaker requires that you bet $110 to make a $100 return. If you see a positive number, that's the payoff you get for a $100 bet. The difference between what you bet and what you get paid for winning is the "juice" or "skim" that I mentioned earlier, which is how the bookie makes his money.
The last line is an "over/under" bet. The number 48 is the cutoff for you to place a bet that you think the total points scored by both teams will be "over" or "under" 48. The money line is again -110, so you have to place a $110 bet for a $100 payoff.