It's a mark of ownership: the father "owned" his children. They were "given" to him by God. And maybe on some tangent, to remind them of what sort of slaves they were, and what sort of slaves they are.
Like a tattoo for a slave....or they usually wore collars or bracelets.
Then it became a mark distinguishing them from gentiles. (those who followed false gods.)
Nice, eh?
It's come to mean a lot of things.
*imagining how guys figured out if they were gentiles*
I guess they were all p*ssing against a wall one day..."oh, hey, you're NOT one of us, are you?"