I'm going to say something counter to what others mentioned. I've used my fixie the past two winter off seasons. It's fun and is a nice alternative to a regular road bike or indoor trainers. But I don't think it helped me improve at all. In fact, trying to force power in a variety of situations got me started on some bad pedalling techniques.

If you want to improve try powermeters, cycling videos with your trainer, one legged pedalling exercises, videos/training books on improving spinning, getting a coach, use rollers, etc.

Fixie's are fun and a good way to keep your riding from getting stale. But I personally didn't find any improvement.