it sounds like your chain tension is low, like the others said. which means that your chain droops a bit, and when you push the pedals, the first few degrees is just picking up the slack in your chain, before it starts pulling on the cog. www.sheldonbrown.com has lots of information on fixed gear stuff and chain tension. what's desirable is long horizontal dropouts or trackends (see that website for definitions); if your axle is at the back of the dropouts, you probably want to take a link out of the chain so that you can get decent chain tension.

it sounds like you bought a bike with what is known as a "suicide hub" by fearmongers--one where a cog and a bottom bracket lockring are threaded together onto a single threading on a non-fixed-gear-specific hub. on a fixed gear, or track hub, there are two sets of threadings. a cog screws on to one, and a lockring screws on to the other, until it's tight against the cog; the lockring is "reverse-threaded" meaning lefty-tighty; so when, under backpressure, the cog tries to screw itself off, it's prevented from doing so by contact with the lockring, which just gets tighter.

hope that helps. now, go to sheldon brown's website and spend hours there. cheers.