Immediately after pitching, the yeast start adjusting to the wort conditions and undergo a period of high growth. The yeast use any available oxygen in the wort to facilitate their growth processes. They can use other methods to adapt and grow in the absence of oxygen, but they can do it much more efficiently with oxygen. Under normal conditions, the yeast should proceed through the adaptation phase and begin primary fermentation within 12 hours. If 24 hours pass without apparent activity, then a new batch of yeast should probably be pitched.
At the beginning of the adaptation phase, the yeast take stock of the sugars, FAN and other nutrients present, and figure out what enzymes and other attributes it needs to adapt to the environment. The yeast use their own glycogen reserves, oxygen, and wort lipids to synthesize sterols to build up their cell membranes. The sterols are known to be critical for enabling the cell membrane to be permeable to wort sugars and other wort nutrients. Sterols can also be produced by the yeast under poor oxygen conditions from lipids found in wort trub, but that pathway is much less efficient.
Once the cell walls are permeable, the yeast can start metabolizing the amino nitrogen and sugars in the wort for food. Like every animal, the goal of life for the yeast cell is to reproduce. Yeast reproduce asexually by "budding". Daughter cells split off from the parent cell. The reproduction process takes a lot of energy and aerobic metabolic processes are more efficient than anaerobic. Thus, an oxygen-rich wort shortens the adaptation phase, and allows the yeast to quickly reproduce to levels that will ensure a good fermentation. When the oxygen is used up, the yeast switch metabolic pathways and begin what we consider to be fermentation - the anaerobic metabolism of sugar to alcohol. This pathway is less energy efficient, so the yeast cannot reproduce as proficiently as during the adaptation phase.
The key to a good fermentation is lots of strong healthy yeast- yeast that can get the job done before going dormant due to depleted resources, rising alcohol levels, and old age. As noted, the reproduction rate is slower without oxygen. At some point in the fermentation cycle of the beer, the rate of yeast reproduction is going to fall behind the rate of yeast dormancy. By providing optimum conditions for yeast growth and reproduction in the wort initially, we can ensure that this rate transition will not occur until after the beer has become fully attenuated.
Worts that are underpitched or poorly aerated will ferment slowly or incompletely due to lack of viable yeast. Experienced brewers make a big point about aerating the wort and building up a yeast starter because these practices virtually guarantee enough yeast to do the job well.