Parti-gyle is an old technique that was often used by small breweries to make a variety of beer strengths. It also represents a good way to efficiently use all the extract value from your grains.
In its simplest terms, parti-gyle gives you two beers from one batch of grain. The first batch is typically a no-sparge high gravity beer, though you can do a small amount of sparge if you want. The second is a weaker beer using the rest of the sparge runnings, often called a small beer. To do the whole process, you need to be ready with two boiling kettles, and two separate fermenters. If you've made a no-sparge high-gravity beer, your mash-tun will be filled with quite a bit of sweet wort. If you then proceed to sparge the tun, you will get a considerable quantity of weaker wort. The Brewing Technique website has a nice chart to calculate both the volume and the gravity of the second batch of wort, which you can find at: http://www.brewingtechniques.com/library/backissues/issue2.2/mosher.html#3 This article gives two different options. The first option will yield a 1/3rd 2/3rd volume split and it good for especially high gravity beers. The other option yields a 50/50 volume split and is good for strong but not quite so extreme beers. Roughly speaking, the second batch will have half the gravity of the first batch.
To do this process right, bear in mind that you have to work out two batches of beer that have similar malt characteristics. For example, an amber big beer will give you an amber small beer. You have the freedom, however, to vary the hop profile and yeast at will, since boiling and fermentation are done separately. You'll have to work out the hop bittering and flavouring for each batch separately. In addition, I'd recommend that you make a yeast starter, at least for the big beer.
At the Big Brew session, we did a Wee Heavy and Scottish Export. Here are some other style combinations that work well together: Barleywine and Pale Ale Imperial Stout and Dry Stout Imperial IPA and American Amber Doppelbock and Oktoberfest
Keep in mind that there are other variations too. For example, you can combine the runnings of two mash tuns if one isn't big enough. In the traditional method of making Scotch, the second running from a given batch is used as the mash water for the next batch of grain. This is how they get a high-gravity wort without any waste. This can also be used to make a truly monster beer. Another variation is to extend the concept into three beers. For example, you can make a Wee Heavy, a Scottish Export and a Scottish Light Ale. Be aware, however, that the more you sparge the wort, the more risk you have of pulling out unwanted tannins and phenolics. Make sure you adjust the pH of you sparge water, especially if you are doing a third batch. And, don't let the sparge water get too hot.