When a student sucks up to his/her teacher it means that they are showing fake flattery or acting like they like the teacher in hopes that the teacher will give them better grades or treat them better.
They hope to get better grades and better treatment by the teacher that the student is sucking up too.
The student is trying to get the teacher to like them or favor them by sucking up to them even though the student may not actually like the teacher.
Some teachers can tell whether or not you're sucking up to them and may punish you or give you worse grades.
So it's really best to not try to suck up the teacher because it can hurt you more than it can help you.
Sucking up to a teacher is just like being a teachers pet.