It links two actions where the first one fetches or takes something and the second does something with it somewhere else. That is the line about picking the meat up and grilling it, and the one about running out of gas and going to find some. The fixed pair 가져다가 드리다, quoted in one line, is exactly this: bring it, then hand it over. Two of the lines here show the bare -다가 instead, which means being interrupted in the middle of an action rather than fetching anything.