Ale is
beer made with top-fermenting
yeast, usually
fermented relatively quickly (a week or two) at
room temperature. This is opposed to
lager, which is made from bottom-fermenting yeast and is fermented more slowly (a few months) in a cooler environment. Because they are quicker to make, ales are much more popular and come in more types than lagers. It's much easier to
homebrew an ale than a lager. Ale yeast, with its short and warm fermentation, leaves a lot more undigested sugars and other flavor compounds (called
esters) in the finished beer than lager yeast, which is more efficient at turning sugar into alcohol. In brewing, this is described as being less
attenuated, and accounts for the heavier body, fuller
mouthfeel, and sweeter and more complex flavor of ale vs. lager.
There are endless varieties of ale, some of which are standard styles, such as bitter, stout, porter, mild and pale (aka "India Pale"), and some of which are merely descriptive, like brown ale, amber ale, dark ale, winter ale... the list could go forever. The factors determining the character of an ale (or any beer, actually) are numerous, and include the amounts and types of malt, yeast and hops used, the temperature of the fermentation, the length of time the wort (unfermented dilute extract of brewing malt) is boiled before yeast is added, the point(s) during the brewing process when hops are added.