A beta-reader is someone whom an author trusts to read his or her stories before they are posted to an archive site. A beta reader can check for anything from spelling and grammar errors to characterization to long-term plot. If you need a beta, you can go to the "writing tips" or "introductions" sections of the forum and make a post asking for one. Say in the post whether you want a beta for just spelling and grammar or whether you want a full story editor.
Authors can sometimes use more than one beta on the same story, especially when the betas have different talents.