The importance of being on time varies from culture to culture, as does the definition of “late.”
In the U.S., especially in terms of school, on time means at the time specified.
If class begins at 9:00, then on time means arriving before 9:00. Late means any time after 9:00.
In a 50-minute university class, every minute counts. The first five minutes are often when a teacher introduces the key points of the day or reviews the key points from the previous class. If a student skips this part of the class, s/he has no idea what is going on. This puts the burden on the teacher to waste valuable class minutes explaining again. Or, since many classes in the U.S. involve pair/group work, it puts a burden on the student’s classmates to catch him/her up.
Too, in terms of cultural values, “Americans” value promptness and believe time=money/some other advantage. Losing five minutes, then, means losing some benefit.
Finally, if you must come late, don’t knock on the door or call attention to yourself in any way.
In some cultures, it is respectful to knock on the classroom door before you enter. Here in the U.S., it is rude. Crack the door open just a little bit to peek in. Then, slip in and sit quietly in the back. (Definitely don’t make jokes or chat with people as you find your seat.) Wait for a pause in the lesson to ask a neighbor quietly for the page number. If the class is small enough that your teacher noticed your late entry, you can apologize after class. Find out what you missed on your own by asking another student. Don’t trouble your teacher for what you missed.
I hope this helps you to understand why being on time to class is a big deal here.