Charles has described the literal meaning. I think that it is mainly used more figuratively though. In that case, it means 'a safe distance away' or even 'as far away as possible'. e.g. "The politicians try to keep the press at arm's length". "When your friends have colds, it is safer to keep them at arm's length."

But I guess you can use it to describe (more figuratively) a person that you don't want to get close to or a topic that you are not comfortable with.

LOL, it means, for example, in the case of keeping a person "at arm's length", to keep him/her away from your body at a distance as far as your arms extended out, just in case he/she decides to suddenly attack you.