It could be a couple of things:

• You have already set the login and password with safari before but may have already forgotten that you did.
• Someone else who borrowed your computer (if its actually shared) may have entered it in.
• Maybe safari assumed to use anonymous login by default and if that does not work it will prompt the user to enter proper credentials.
• For some reason the site owner may have decided to block certain browsers for some weird reasons.

It also doesn't really help if you cannot tell us which site you're referring to in the first place.