If you look at the scores of everyone who takes the SAT in a given year, the average score would be somewhere in the vicinity of 500 per section (Critical Reading, Math, and Writing), or 1500 total. So if you scored around 1500, you can assume that somewhere around 50% of the students who took the test in the same year did better than you, while the other half did worse. Speaking very generally, if you are one of the lucky 50% of students who did perform better than average, you should be proud. You have reason to believe that you did well on the exam.
If you're evaluating your scores and it's your first experience taking the SAT, note that nearly every student who takes the SAT multiple times performs worse on their first try than on the subsequent ones. So don't cry yourself to sleep tonight if you scored below 1500. Give the exam another shot.
Of course, different colleges and universities have different admissions standards, so how do you know if you'll get into the college of your choice with your current SAT score? That's a tough question to answer because most colleges are very reluctant to pick a number and steadfastly say that they won't consider admitting a student who scores below it.
That said, just as examples, one source says that to get accepted into Harvard, you need either a minimum score of 700 per section or a total score of 2200, while another source claims that students applying to Indiana University should score at least 550 per section or 1650 total.
But again, don't hold these numbers as gospel truths. It's unlikely you'll have the door slammed in your face if your SAT scores fall slightly below whatever number you've read or heard that the college you want to attend is looking for. College admissions offices look far beyond test scores in determining whom to admit. Also important — or even more important than your SAT score — is your class rank, your grade point average, and your course load. Still other things that play a factor are your involvement in clubs, sports, and activities, recommendations from teachers, and even your personality (energy, self confidence, and enthusiasm).