Temperature, pH, aerobic condition, contamination are all factors which can cause distress to yeast. When stressed, yeast can reproduce poorly, die off, and create off flavors. It is typically considered bad process to induce stress in yeast.
There are lots of different types of stress. Some of them include:
1) Osmotic stress
When you pitch yeast into very high gravity wort, it can osmotically shock the cell and damage it, resulting in low viability and vitality following the pitch.
2) Temperature stress
When a yeast is temperature shocked (extreme temperatures or temperature fluctuations), there is a good chance that there will be a alteration in the rate of gene expression and protein synthesis. As long as the temperature is not below freezing or above the point at which significant cell death will occur, the yeast can typically recover, though you may get some cell death, decrease in vitality and additional lag in fermentation. Constant temperature fluctuation will likely result in a constant start/stop to gene expression and protein synthesis, which may cause the yeast to either incompletely ferment your wort or take a very long time. A cautionary note though, different strains will almost certainly exhibit varying degrees of stress at a given temperature. I would think that this is fairly strain dependent.
3) Oxygen stress
When new yeast cells are being produced, the cells require oxygen to make sterols and unsaturated fatty acids that are integral components of the cell membrane and give it integrity and the necessary physical properties requires for healthy cell function. If the yeast are in low oxygen during a period of rapid division and cannot produce these molecules, the cell membrane in both existing and new cells will be weak and have poor physical properties, and the vitality of the cells will be fairly low, resulting in poor fermentation characteristics.
Yeast have a job to do, and that is to convert sugars to alcohol and CO2. Like any organism, yeast will wear out if overworked, and using too few yeast to complete a job will result in yeast prematurely ceasing their duties, often resulting in high gravities and "stuck" fermentations.
There are a lot of different types of stress. These are just a couple of the main ones we experience and want to combat.