Students start by creating an account on the University and Colleges Application System (UCAS). All the universities are on there, so unlike the USA system where you have to fill out separate applications for every university, UK students just fill out one. They have to write a personal statement summarizing why they want to apply for the subject they've chosen, and they choose the programs to which they want to apply. In the USA you apply to the university and don't actually have to choose a major yet since everyone takes the same classes in the first semester anyway. Not so in the UK.
So, you have to choose your field of study. If you want to study physics, you find programs that appeal to you. There's a great variety even within a field. Physics, Physics with Philosophy, Physics with Maths, and Natural Sciences are all examples that might appeal to a physicist. You are ultimately restricted to 5 programs on your application.
Students choose programs partly based on what they want to study and partly based on how difficult it is to get into the program. This is where it gets complex, because remember, they don't take the exams until the end of the year.
Classes taken in the last two years of high school (called Sixth Form) are A-level classes. Students only take 3 or 4 of them. At the end, they take exams and earn grades of A*, A, B, C, D, E, and so on. After applying to the universities, students don't get accepted as such, they earn offers. I might apply to a physics program and get an offer of AAB, which means those are the grades I need to earn. It doesn't generally matter what exam gets what grade, although a physics program could require me to earn an A in my physics exam. If a student gets an offer and earns the grades, he/she is accepted into the program. If not, then not.
During the application process, students look at the normal grades needed for offers from that program. Universities will only make offers to students likely to match them, so we teachers are asked to make predictions of what grades they will earn. We make these predictions with a year still to go in their education. If you give an honest appraisal that isn't as high as the student had hoped, it could be deflating. It could also be motivating, but if the students predictions are all too low, it lessens their chances of getting offers from some programs. On the flip side, if you err on the very hopeful side, predicting higher than you reasonably think they'll get, it can prevent students from seeing how far they need to go to reach that plateau. If a student has overly optimistic predictions, he/she may be likely to fall short of any offers, leaving them in limbo when the grades come in. On top of it all, universities will often make offers higher than they actually want. Let's say Schneider University is happy with students getting ABB. We may choose to only give offers of AAA in order to get smarter kids applying. If students earn at least ABB, we'll accept them anyway. But if they don't have the AAA predictions in the first place, we won't give them the offer.
These predictions are one of the quirkiest parts of the UK school system from an outsider's point of view, and the stakes make it an emotional part.