Yeast are small single cell organisms. It is everywhere you can imagine. When making beer the yeast we are referring to is Saccharomyces cerevisiae for ales and Saccharomyces uvarum for lagers. There are many strains of this yeast to obtain different flavor profiles. There are other types of yeast and bacteria that one can use in brewing. Lambic styles call for some different bacteria that wouldn't normally be used in making beer, thus lending the sour taste that lambics are known for. Yeast can be purchased in dry or liquid suspension forms. The liquid yeast gives the brewer more control over the flavor profile. You can also culture your own yeast from starters or obtained from other beers.
Ale yeast, which is top fermenting, tends to make a soft or sometimes fruity beer, while lager yeast, which is bottom fermenting, can make it dry and crisp. Ales ferment at higher temperatures (66 - 74° F) than do lagers (45 - 65° F). The lower temperature prevents the fruity flavors from being absorbed.
You may find some discrepancies in the yeast names. In some places the name Saccharomyces carlsbergensis is used. This is just an older name for Saccharomyces uvarum. In other places, you may not see either the calsbergenesis or uvarum names. Recently the powers that be did some regrouping of the names and put them together under cerevisiae.
As yeast feeds on the sugars in the wort they reproduce. After fermentation starts a layer of foam will be present in the fermenting vessel. This will soon turn into a rocky, dirty looking head that can vary in size. A lot of carbon dioxide is being produced and if the fermenter is not able to expel this it can explode. A blow off tube may be a good idea if you have high gravity wort.