What does the idiom 'get your walking papers' mean?

Someone getting their walking papers is just like getting "the pink slip". It means he or she has received his/her notice of termination (the "walking papers" or "pink slip") and is no longer of the company.

The idiom of "getting walking papers" has been extended beyond the workplace and into other social situations: in which case it generally means the recipient is being told to get lost and don't come back. For example, a girlfriend dumping a cheating boyfriend can be said to be "giving him his walking papers".