Office hours are a set time before or after class an educational instructor- usually a college professor- sets aside for students to come in and ask questions or get extra help on their lessons. These are usually more limited than, say, advisory or tutorial times in modern high schools. In case you don't know what those are, it's a similar concept where a student has a "homeroom"(/avisory/tutorial) teacher whose classroom they go to for one period in a day, or they can go to another teacher's room to do things like ask questions & get help, make up missing work, do tests they weren't there for etc etc.
I personally find homeroom and office hours very nice, because it gives me a good amount of time to knock out my homework that I've gotten for the day so far, and apart from that I can make some progress on iron noder. However, they have recently stopped allowing us to visit other teachers, which kind of defeats the purpose, because some kids were saying they were going to one class but actually wandering the halls or going to visit their friends in another class.
Talk about throwing the baby out with the bathwater.