A unit in sports betting is a measurement of the size of a given bet. It's mainly used because everyone's bankroll is different and a unit refers to the percentage of a bankroll. One unit is usually equal to one percent of a bankroll, though it's not the same for everyone.
For example, if your bankroll is $1,000, one unit would be $10 or 1%. In this situation, if someone puts three units on a bet, it would be a $30 bet.
If you're a serious bettor, it's rarely a good idea to make a bet with more than five units unless you know something everyone else doesn't. Often, a one-unit play compared to a five-unit play is in reference to a bettor's confidence. If you really like a certain bet, you can lay five units on it.
If you're not a serious bettor, units aren't a major deal because you can go into a sportsbook with a set amount of money and bet it all in one night. Maybe you won't spend all of the money on one bet, but if you keep losing, a $500 bankroll can disappear fairly quickly if you're making $100 bets.
Units are often what matter most in the betting world, at least for bettors who share their statistics (like touts). Someone could have a 10-0 betting record and be up 10 units, but a person with a 4-6 record could be up more units if they played their cards right. That's because the four wins could all be five-unit plays, but the six losses are just one-unit bets, making the total tally up 14 units. Either that or the bettor with a 4-6 record was betting on a lot of underdogs and four of them hit.
While having a good record is nice to show your friends, the amount of units you're up is what technically matters most, and it's usually what people in the betting world use.