Moderators have the ability to edit, move and delete posts, open and close threads, sticky threads, split and merge threads, change thread titles and edit poll results. They can also validate posts waiting in the moderation queue, suspend users, view user details, and manage user groups.
In addition to the above, admins have full control over all the site variables, templates, files, datasources etc.
You can find out more (including admin demo) on the Vbulletin web site.
How mods are chosen.