Used to refer to something or someone random, or of no particular importance, or even someone or something you might dislike.
The 'ass' part has no meaningful contribution and is therefore a random ass addition.
Sally: "Where's Paul"?
Martha: "I dunno, he left with some random ass girl from next door."
I was walking down the street the other day when some random ass guy walked up to me and asked me if I had seen his dog. Wtf.