Hippy's right. In a fermentation, the yeast uses up the sugar, making alcohol. When the alcohol builds up too much, the yeast stops growing, then eventually dies.
The exact amount of alcohol which does this varies according to the strain of yeast. Some wine yeasts can keep working up to as much as 17% ethanol -- others will stop long before -- perhaps around 10% (search on "alcohol, tolerance, yeast").
This is how sweet wine (ugh!) is possible. Although there is plenty of sugar left, the "yeastie cells" are all snoozing happily under the affluence of inkerhol. (Usually though it will also be pasteurised, to make certain they don't start up again for a while and explode the bottles...).
Incidentally, it's not true, as some people believe, that alcoholic drink becomes magically stronger the longer it's kept. Once the yeast has stopped and the drink's bottled that's generally it.