Should I use a wort chiller, and what are the advantages of doing so?
You should if you can. The advantages are a faster brew-day, a shorter window of potential wort contamination, and a better cold break. (Depending on the method, you might also get improved clarity due to whirlpooling trub and break material that you would then not siphon in the primary fermenter.
It's basically coiled copper tubing you run cold water through to help cool your wort faster. I built the one I use. Anybody that's run an old musclecar would have recognized it as something akin to a "cool can". I have brass fittings at each end of the coil that attach to hoses. One I affix to my tap, the other drains into the sink.
You prepare your wort as usual, then at the final few minutes of boiling, drop the coil in. This helps sanitize it, but obviously it should be cleaned beforehand. When you've turned off the heat, you start running the water which goes through the coils and down the drain. The reasons/benefits were summed up nicely in jsled's post.
The advantages of chilling your wort is to be able to pitch your yeast more quickly, thus shortening your brew day. Also, your wort is susceptible to bacterial infection if there is no competing yeast. There are many people, especially those down under, that have no problem letting wort cool in it's own sweet time, but it seems that most brewers here are interested in chilling quickly.
There are two kinds of chiller:
- Immersion Chiller - A coil, typically made of copper, where cooling water flows. This picks up heat from the wort and carries it away.
- Heat Exchanger Chiller (reverse flow chiller) - Can be a plate chiller or a tube inside a tube. The cooling water flows in the opposite direction as the wort, so the coldest chilling water exchanges heat with the coldest wort.
Immersion chillers are the simplest type of chiller. These will be much more effective if they are agitated during chilling (this prevents a layer of cool wort from staying next to the coil).
The heat exchangers can be used in a single pass, where the wort goes through once, and into the fermentation vessel, or can be used in a recirculating mode (needs a food-grade pump) where the wort is returned to the boil kettle. In the single pass configuration, the cold break ends-up in the fermentation vessel, but has the advantage of not requiring a lot of attention (no agitation), and no pump (if your burner is up high enough for gravity to allow the kettle to drain into the fermentation vessel.
A wort chiller is something you use to cool your hot wort to pitching temperature. A copper coil submersion chiller is a pretty common type of wort chiller for home brewers. In addition to what jsled mentioned for reasons of using one, it can also help reduce DMS buildup in your wort since it is still being produced at hot temperatures even though it's no escaping through steam.