Saccharomyces cerevisae is the yeast (a type of fungus) that ferments the sugary wort into beer and makes bread rise by generating carbon dioxide.   Saccharomyces is derived from the Greek for "sugar mould" and Cerivisae from Latin for "beer".

There are many strains of this yeast but all come under the Saccharomyces cerivisae heading.   Saccharomyces carlsbergenisis is used by the famous Danish brewer to describe their lager yeast which they pioneered in 1883.   Other people call lager yeast Saccharomyces pastorianus.   Saccharomyces brettanomyces is a wild yeast (ie abundant in nature but not desirable in breweries usually) that gives lambic beers their sour taste.

Birth

S. cerevisae is a single celled organism with a nucleus, organelles and a cell wall.   It breeds by budding - the cell undergoes mitosis and an identical daughter cell is formed on the outside of the cell wall.   This drops off leaving a budding scar.   The age of a yeast cell can be estimated by the number of scars on its surface.   An original yeast sample is kept cryogenically frozen in a lab and pure strains are bred from it and sent to the brewery periodically to ensure than contamination and mutation doesn't introduce off-flavours to the finished beers.

Life

Yeast metabolise glucose aerobically (with oxygen) via the following simplistic mechanism:

C₆H₁₂O_{6 +} 6 O₂ → 6 CO₂ + 6 H₂O + energy

glucose + oxygen → carbon dioxide + water + energy

For brewing though, the anaerobic (without oxygen) route is taken:

C₆H₁2O₆ → 2 C₂H₅OH + 2 CO₂ + energy

glucose → 2 ethanol + 2 carbon dioxide + energy

The aerobic path generates much more energy than the anaerobic one but doesn't produce beer!   The glucose comes when the maltose sugar from malt is broken up into two glucose units.   A little oxygen is needed at some point in the fermentation process as the yeast needs it to synthesise building materials for budding. 

Wort is not just a sugar solution though, as proteins and salts are needed for yeast to be healthy.   The yeast uses these to produce acids, esters, higher alcohols, sulphur compounds.   These compounds produce much of the flavour in the finished beer, but not all are desirable.

Acids such as citric and acetic lower the pH of the fermenting wort, producing beer which has pH of around 4.

Esters such as Ethyl Acetate and Butyl Acetate produce flavours described as solvent, fruity and banana-like, sweet respectively.

Higher alcohols are alcohols with longer carbon chains than ethanol, such as propanol and butanol.   Tiny amounts present can give a warming solvent-like taste.

Sulphur compounds such as ethyl mercaptan and dimethyl sulfide give a rotting vegetable or overcooked cabbage flavour.   These compounds are particularly important as they can be detected by humans in the order of parts per billion.

Death

As the nutrient source runs out towards the end of fermentation, yeast cells die and flocculate towards the bottom of the fermentation vessel.   Here they will undergo autolysis and leak their contents into the beer.  The most important of these is diacetyl, which gives a butterscotch off-flavour that is detectable even in low quantities.   The remaining live yeast cells will mop up this compound given time.  

In lager fermentations where the reactions take place slower due to the cooler temperature, the temperature is increased to that of ale brews for a short while at the end and is called the diacetyl break.

The remaining yeast may be added to another batch of wort for fermenting, stored for future use or sent to the manufacturers of yeast extract spread.   If stored, the yeast will need periodic access to oxygen and an addition of acid to prevent bacteria growing alongside it.