Separating eggs is a process, generally used in cooking, in which the egg yolk is removed from the egg white. This allows one part of the egg to be used without the other part, or each part to be treated in different ways. Recipes for custard call for egg yolks, for example.
The most common reason for separating eggs is so the whites can be whipped. Also, because cholesterol is only found in the yolk, using only egg whites in a recipe will drastically reduce its cholesterol content.