There is always some overlap, but the term "Lager" means to ferment in the cold. Around 50-degrees for primary, and 35 degrees for conditioning. Ale yeasts do not like to go below 60-degrees, so special lager yeast designed for the cold is used.
The benefit is less flavor. Ale yeasts produce lots of esters (fruity flavors), as well as fusals, and other flavors. When using a lager yeast in the cold, you generally do not get any flavors, so you taste just the malt and hops (and sometimes sulfur).
Beyond that, there are stylistic differences. Lagers tend to use less hops then ales, and tend to use Germanic ones (ie Saaz). Likewise, they tend to use Lager malts, and tend to favor certain water salts, to enhance, or diminish certain flavors.
Lagers are tough because of the temp control requirements, but you can USUALLY make pretty good lagers by doing your primary ferment in the basement, then bottling without a secondary, so you can condition in your fridge with all your groceries. (if your wife allows).
nick