Coopers ales use a special brewing process in which the second part of the brewing occurs in the bottle. This is similar to the fermentation process of Champagne. The residual yeast is a direct product of this process.
The correct way to drink a Coopers ale is to first invert the bottle, allowing the yeast sediment to mix through the beer. Only when this has been done should the beer be opened, allowing you to fully appreciate its great flavour. Should you ever visit South Australia you risk being shunned if you say "eew, look at the crap in my beer!" and try to avoid drinking it.
One of the most amazing things about Coopers is that they have been using the same yeast for nearly 100 years. That is to say, each batch of yeast is derived from the last, so basically the brewery has been using one neverending culture of yeast since the turn of last century. The brewery periodically takes samples of the yeast and stores it in spore form to protect it. The same batch of yeast even continued after a recent factory relocation!
Coopers beer is also brewed using only the essential ingredients for producing the beer itself, and no additives or preservatives of any kind (similar to German beers). This supposedly reduced the risk of a bad hangover, although I can produce many witnesses who would claim not enough.
While Coopers main market is South Australia and Australia it can be found overseas and I urge you all to try it. I can confirm through personal experience that it is available in the Australian-themed pub in Edinburgh and in at least one bar in central Paris, as well as various pubs in England.