It's actually quite simple.  All beers are either ales or lagers.  Ales are the older and more traditional brews, predating lagers by thousands of years.  Ales usually ferment in warmer temperatures (12 to 21 degrees Celsius), while lagers ferment at between 3 and 10 degrees Celsius.  The cooler fermentation of lagers inhibits the production of fruity aromas (called esters) that are characteristic of ales.  This gives lagers a cleaner, crisper taste.

Ales generally are more robust tasting, are fruity and aromatic, include more bitter beers, have a pronounced, complex taste and aroma and are usually enjoyed warmer (7 to 12 degrees Celsius).  Typical ale styles include Porter, Stout, Brown Ale, Amber Ales and Pale Ales.  Wheat beers are usually categorised as ales.

Lagers generally are lighter-tasting, tend to be highly carbonated (or crisp), are smooth and mellow, have a subtle, clean, balanced taste and are served cold (3 to 7 degrees Celsius).  Lager styles include Pale Lager (Pilsner), Amber Lager, Bock and Dark Lagers