달리다 is running, and the -아서/어서 clause gives the reason or the manner: 그 장면을 위해서 달리는 거예요 (I run for that scene), 나가서 달리는 거예요 (go out and run). It applies to vehicles as well as legs — 비포장도로도 조심해서 달려야 되는데 is about driving carefully on unpaved roads. 미쳐서 달리다 is going at something like mad.