A fixed gear bike (like those used for track racing) forces you to feel the pedaling motion throughout the entire 360 degrees. It’s a great way to develop the habit, or muscle memory, of moving the pedals in complete circles rather than just focusing on the down stroke.
If you haven’t ridden a fixed gear bike before I’d recommend starting out on a stationary trainer until you get accustomed to the fact that you can’t coast or pedal backwards (actually, you can pedal backwards, just not while you’re moving forward). For most, just riding a fixed gear bike on an indoor trainer will be sufficient to help them develop better pedaling mechanics. For the cyclist that specializes in track racing, ridding a fixed gear bike out on an endurance/muscle endurance ride will be useful as well. Be sure that you’re comfortable on such a bike before attempting to ride on public roads. Be sure that the bike has a brake!
As with other drills on the indoor trainer, listen for the smooth, constant whoosh that indicates a continuous amount of force is being applied to the pedaling motion.