An over/under is the total number of points, runs or goals in a specific game. For example, the over/under between the Los Angeles Lakers and Boston Celtics is 230.5 points. If you think it will finish with more than 230 points, you can bet the over. If you think those teams combine for less than 231 points, you bet the under.
This is usually the kind of bet you make if you don't prefer either of the teams, as in you don't have a good feel for either of them to win outright. For the above example, you could bet the over if you think neither the Lakers nor Celtics are going to play defense. In the opposite mold, if you think each team will play tight and tough defense all game, the under may be the better option.
Overtime is only good if you bet the over because it doesn't change your bet. It doesn't matter if the game ends in regulation or a fifth overtime, your original bet is what counts. So if that Lakers and Celtics game goes to overtime at 115-115 and you bet the under, you're unfortunately out of luck because more points will be scored. Of course, if you bet the over, you're in luck and are all but guaranteed to hit.