Another Earth is a excellent and original story that explores some similar concepts of science fiction. The story's core ideas deal with the perceptions of what it would be like actually meet yourself. Similar ideas come from movies like The 6th Day, Moon, Resident Evil, and many more. All of these films have the common theme of meeting yourself as yourself.
What is interesting about Another Earth is that it keeps you in the dark about what might be on the other planet until later on in the movie. Rhoda, the young girl, soon understands that what she is doing to try and make up for causing the death of John's family is not the right thing to do, but to let him go to the other Earth and find his family.
Another interesting idea is the fact that these people do end up going to the other Earth, but what is the first they do? They go and find themselves once they are on the other planet. What is so interesting about meeting ourselves? We see ourselves every day, so what would the difference be if we were to actually see a clone of ourselves? Perhaps we would be judgement like some people are of others. Maybe it is to show how the small things we do in life can change dramatically. Rhoda's life did with a simple advertisement on a radio station. The moment Rhoda from the other planet appears you know that she was the successful one.
Something interesting to consider is what might actually happen if we were to actually meet ourselves. In Rhoda's situation there might be questions to ask back and forth about how their lives differed. But the real problem is what might happen after you meet yourself. Is it really a clone of you once you start interacting? Wouldn't we just become very similar people instead of clones? Perhaps the outside judgement of ourselves makes us take on a completely different character than we were before. That is an interesting idea to think about that we will, unfortunately, probably never get to experience.