A lottery is just a fair way of choosing new students. Suppose a school has, say, 300 openings for new students, but they have 1500 applications. The easiest thing to do is to throw 1500 applications into a box and have someone pull out 300 of them with their eyes closed. Everyone has the same chance as everyone else. These days, they'd do it with a computer--pick 300 names at random from a field of 1500. That's a lottery.
The alternative is to make choices based on points. You get a certain number of points for how well you did on your last report card, you might get points for where you live or what race you are, or what special aptitudes you have or whatever. Some schools do this, but there are always complaints that the point system is unfair. A lottery where everyone has the same chances, that can't be unfair.