When you're playing a game, your score is the number of points you have. If the score of a basketball game is 34 to 34, it means both teams have 34 points — the score is tied.
To score in a game is to achieve points or goals. In school, you get a score, or a grade, on your tests and papers. Another kind of score is the written part of a musical composition. And when someone asks, "What's the score?" they might also mean "What's going on?" The Gettysburg Address famously begins, "Four score and seven years ago..." In this case, a score is "twenty," from the Old English scoru, also "twenty."