Chris has the answer. If you say "we went back home," then it's clear that you went all the way back home. If you say "we headed home," it means you started to go home. To "head" for a place is to go in the direction of that place. It doesn't necessarily mean that you will arrive at the place. For example:
"We headed for the theater, but there was too much traffic, and we realized that we were going to be late. We ended up going to a restaurant instead."
In this example, the speaker "headed" for the theater, but did not actually go to the theater.
Usually, if you don't add anything else to the story, people will assume that you successfully arrived at the place that you were "headed" for. Sometimes "to head" can make a sentence sound more casual.