To run along means to "go along one's own way" .... your own path. So to run "along" means to > leave and go in your own direction. Hurry along means the same thing. Hurry and > go in your own direction.

Well.. It's confusing. I mostly see it used by parents ><;; saying "Run along" to someone means you want them "hurry up and leave\go" because they're going ot be late or you just don't want them around. saying "Hurry along" means the samething almost, just without a verb. ex: Kid: I don't wanna go to school!! Mom: You're going, run along now. (You're going, so hurry and leave) Like I said, I only see it used by mothers talking to their kids haha. IT can be used by kids\teens though. Apparently in Korean they're "따라 실행해" & "따라 서둘러" XD (I asked my friend)

along in this case means go. For example: Mom: Time for school! Son: I'm trying to find my homework. Mom: Here it is, run along now or you'll be late.