A "tie" is when two sides in a competition have an equal number of points or qualities. A soccer game is tied if the score is 3-3. A vote on an eight-member committee can be tied if each side has four votes.
Something can "break the tie" if it gives one side an advantage, after both sides were tied. For example, in the World Cup final, the score was 3-3 after regulation time and an overtime period. Under the rules of the World Cup, a series of penalty kicks would break the tie. In the 2022 final, Argentina won the penalty kicks and the tie was broken.
The U.S. Senate has 100 members, two Senators from each of 50 states. The Senate's rules are complicated, but it's possible to have a 50-50 tie, where 50 Senators vote one way and 50 Senators vote the other way. In this situation, the American vice-president can cast a vote the break the tie. (The VP does not vote unless there is a tie.)