"Skipped" the class last week implies that the individual purposely did not go to class because he or she did not want to go. "Missed" the class last week is more broad and could be the individual did not go because they had something actually important to do, like a doctors appointment, a job interview, or a funeral. Both of them mean the same thing, but the way they are used in society imply different things. For example I might tell my friend "I skipped class last week, just didn't really want to go." But, I would tell my teacher "I missed class last week for personal reasons, can I make up the quiz?" You wouldn't tell your teacher "I Skipped class" because it sounds bad.

"I skipped class" has means that you could have went to class but you did not go to class because it was not important to you. You wouldn't say "I skipped class" unless you wanted the listener to know that you did not care about attending the class. "I missed class" means you did not go to class because, although you consider class important, you had to do something you consider more important.

Skip - intentional, on purpose Miss - by chance or circumstances that don't depend on a person