rm is the simple remove command.
rm -r is recursive and it will remove anything you ask it to and anything inside that, provided it has permission to.
rm -rf is the same as rm -r except that it doesn't ask what it's allowed to do if it has any questions, it just tries to do it any way without asking.
rm -i is interactive remove, so it asks at every item.
rm -ir is interactive and recursive, so it asks about everything, and everything inside everything.
If you're fearful about what you might be deleting, it's really useful to have it prompt you. My school aliases rm to 'rm -i' so that everyone gets interactive delete. It keeps people from shooting themselves in the foot.