The user password, if set, is what you need to provide in order to open a PDF. Acrobat/Reader will prompt a user to enter the user password. If it's not correct, the document will not open.
The owner password, if set, controls permissions, such as printing, editing, extracting, commenting, etc. Acrobat/Reader will disallow these things based on the permission settings. Acrobat will require this password if you want to set/change permissions.