When a block is appealed, other editors – most of whom probably have no involvement in the matter – will review your editing history, which has been logged, as well as the reason for the block and the history leading up to it. Requests for unblocking are listed at [[Category:Requests for unblock]]. To appeal a block add
Special:IPBlocklist contains a list of all currently blocked users and IPs. Admins will see a link to unblock next to each user. After clicking this, you should type in the reason that you are unblocking the user and then click the Unblock this address button.