I've been biking on single-speed for a few months and would like to play around with a fixed gear. I've heard of a flip-flop hub, but I'm not sure exactly what it is. And without any fellow bikers - I'm completely lost.
Benzo and Glenn Gervais are right on, but I thought I'd include a photo for any visual learners. This is a typical fixed/free, high flange rear hub. Quite often they're available in 120mm and 130mm OLD to fit different width dropouts. These hubs generally have solid axles without quick releases to prevent the hub from slipping and slackening your chain.
The right side is for a fixed cog. (The hub in the picture has a lockring installed already). The left side is for a single speed freewheel.
Below is another example (a White Industries ENO Eccentric) with two big differences. First, instead of two opposite-threaded areas for a cog and lockring, this hub has splines for a splined cog and threads for the lockring (left side of the picture). The second difference is the eccentric axle which allows for chain tension adjustment on bicycles with vertical dropouts (single speed or track specific bikes have horizontal or rear-facing dropouts for chain tension adjustments).
If you have a singlespeed, you may already have a flip flop hub. A flip flop hub has threads on both sides of the wheel. Typically there is a side for a freewheel and a side for a fixed gear. Take a look at the rear hub opposite the freewheel and chain.
The fixed gear side will have two tiers of threads, one larger diameter section for a fixed cog and a smaller diameter section for a lock ring which is reverse threaded. You need to thread on the fixed cog clockwise, then thread on the lockring counterclockwise.
You do not want to attempt to put a fixed cog on the same side as the freewheel if it does not have the reverse threading for a lock ring. This is known as a suicide fixed cog because you can't put a standard fixed cog lockring on and would have to use a lockring from a bottom bracket typically to prevent the fixed cog from loosening when backpedaling or skidding. Over time this can come loose and cause you to loose the ability to brake with the back wheel as the cog will unthread as you backpedal.
You can however thread a freewheel on to the fixed side of a hub with no real issues. This would thread on clockwise like the fixed cog. No lockring would be used. This can be common when using fixed / fixed hubs which are threaded for a fixed cog and lock ring on both sides.
Flip-Flop hubs have freewheel thread on one side, fixed-gear threading on the other side. Many SS bicycles come with this sort of wheel, if you have a sprocket on both sides of your hub, you already have a flip-flop hub/wheel.
If you only have a single sprocket (and it is a fixed gear hub, see note below), you can purchase a fixed sprocket and replace the SS freewheel with the fixed sprocket, since both singlespeed and fixed gear hubs use the same 1.37 x 24 tpi threading for the sprocket.
Note: @heltonbiker is correct, you will need a lockring with the fixed gear hub, they have a double thread, one for the sprocket and one for the lockring. You can put a SS freewheel on a fixed gear hub, but you cannot put a Fixed sprocket onto a SS hub (it does not have the step down threading for the locking mechanism)