Yeast is the life force for making beer. Although this ingredient is by far the most mysterious to home brewers it is has so much influence on the flavor that some breweries maintain their own strains and keep them on lock down...top secret. These microorganisms are hungry, and they love sugar. The bi-product of this appetite is simple: alcohol, co2, and energy (heat).
Before the power of yeast was truly realized, the fermentation and production of alcohol seemed to be magical occurrence. Aging wort left open to the elements would gather natural yeasts from the air and atmosphere. These yeast had the same common objective as the strains used today, to eat. However the old world approach obviously has its disadvantages. Everything else in the air, including oxygen, bacteria, and other organisms also found its way into the wort. This reduced the predictability of the flavor.
Yeast for brewing comes in two major classifications for brewing; top fermenting and bottom fermenting. They are names as such due to the where they settle during the fermentation process. Although the definition of an ale and lager is not based on the yeast, these types of beer do generally use the varying types. Lagers are generally brewed with bottom fermentting yeast. And this is due to their vitality at different temperatures (lagers ferment at cooler temperatures).
Yeast is very often recycled and reused after brewing. For the homebrewer the technique is simple and can be accomplished by saving some beer from the bottom of the fermentation tank. For the breweries its similar, however the equipment is generally designed for easy extraction. The reuse varies on the quality of the preservation and extraction process. For homebrewers this can be from 4-6 times. The professional brewery can go as high as 10-12. After this the risk of ruining a batch by not having enough active yeast starts to become too great.