I never thought of them as competing against someone else. This was my motivation. Actually placing or winning was always nice, and I admit, a bit addictive. Any addiction will lead you to do more of the same, and I continued to enter contests consistently for 2 years. Only recently did I lose the real need to compete.
Many writers enter a competition simply to prove something.
If they can win or place, they have proven they can accomplish this, and they are a good writer. Taking this one step further, many writers only enter these competitions to see if they are good writers. This is dangerous. If you enter a competition knowing you may not win, and you are alright with that, then there is no harm no foul. But if you fully anticipate winning, and losing means to you that your work is unworthy, this can lead to major problems down the road.