This is a good question.
The word, "incumbent," is usually used in the context of elections. It is used specifically to describe the current holder of office. So, in our next presidential election, President Obama will be the incumbent. The person, whoever that might be, who runs against President Obama will be the non-incumbent.
This point is also important to konw, because historically speaking the incumbent has a few advantages. For example, since he or she is already the holder of office, he or she has more recognition. In addition, because the incumbent holds office, he or she will have the advantage of setting the election schedule rather than the non-incumbent.
In the instance where there is no one in the existing office, the election is called an open seat.