"Hin" usually refers to an activity directed or oriented away from a subject or an object considered towards another (accusative) object, while "her" refers to an activity directed or oriented towards a subject or a considered object.
A few examples:
I saw them running to the scene of the accident. But they came back to me again immedeately - Ich sah, wie sie zur zur Unfallstelle hin liefen. Gleich darauf kamen sie aber wieder zu mir her.
Look at this carefully! - Sieh genau hin!
Look my way/at me when I explain something to you! - Sieh her (alternatively: Schau her), wenn ich dir etwas erkläre.
Hm, good question. I'd simply say that the first version is colloquial and the second one is supposed to be the standard version, as you should learn it. "laufen" and "hinlaufen" usually mean the same action.