A Facebook user blocks you on the site when she does not want you to have any access to her profile or content she posts. Because it would be a departure from the intention of blocking, you are not informed about being blocked or able to see which users blocked you.
When another Facebook user blocks you on the site, you are placed on her block list. Each user's block list is completely private, visible only via the "Privacy Settings" menu in her account, which other users do not have access to. A block list only contains the list of people a user has blocked herself and not the people that have blocked her.
Facebook does not notify you when another user places you on her block list. If you were friends with the user on the site, your friendship is severed, and she no longer appears on your friend list. Just as when someone defriends you, you may notice that the number of your friends has been reduced, but Facebook does not point out who is now missing from the list.
Once a user places you on her block list, all references to her on Facebook are made invisible to you. You cannot search for her on the site, see her comments on other users' profiles or view any part of her profile. All types of communication with her are blocked. The only way your communication can be restored with a blocked user is if she decides to remove you from her block list.
Do not try to get around a block by creating a new account under a different name so that you can once again see a user's profile information. Facebook prohibits you from using fake names on the site, and the user may report you for abuse if you continue to send unsolicited messages or friend requests. Just accept the block and hope the user chooses to lift it at some point.