There is very little in the school curriculum which has proof as a focus, whereas proof will take centre stage in all of university mathematics. A proof is any structured mathematical argument where each step follows logically and precisely from the previous step.
It takes a while to get used to reading and constructing such arguments. When dealing with proofs you will need to be careful and very patient to be sure that the argument holds at each step. If you spend time working on proof issues at school then you will be able to get a feel for university mathematics and give yourself a head-start at the beginning of a university course.
These related problems will get you thinking hard about proof and clarity of thought in mathematics: