Separating eggs is a process usually used in cooking

Cooking

Cooking is the process of preparing food by use of heat. Cooking techniques and ingredients vary widely across the world, reflecting unique environmental, economic, and cultural traditions. Cooks themselves also vary widely in skill and training...

, in which one removes the egg yolk

Egg yolk

An egg yolk is a part of an egg which feeds the developing embryo. The egg yolk is suspended in the egg white by one or two spiral bands of tissue called the chalazae...

 from the egg white

Egg white

Egg white is the common name for the clear liquid contained within an egg. In chickens it is formed from the layers of secretions of the anterior section of the hen's oviduct during the passage of the egg. It forms around either fertilized or unfertilized egg yolks...

. This is used to allow one part of the egg to be used without the other part — for instance, many recipes require frothing egg whites to make a foam, which will not work if the yolk is also included, as fat

Fat

Fats consist of a wide group of compounds that are generally soluble in organic solvents and generally insoluble in water. Chemically, fats are triglycerides, triesters of glycerol and any of several fatty acids. Fats may be either solid or liquid at room temperature, depending on their structure...

 prevents eggs from foaming. Since egg yolks are high in fat, it is best to separate them before whisking.

Methods

All methods for separating eggs make use of the fact that the yolk can hold itself together while the white is much more runny. Since older eggs have more watery yolks which make separation difficult, it is a good idea to begin with the freshesthttp://www.hormel.com/templates/knowledge/knowledge.asp?catitemid=2&id=185#Freshness eggs available. Old eggs can be used for other dishes that do not require separation, like omelette

Omelette

In cuisine, an omelette or omelet is a dish made from beaten eggs quickly cooked with butter or oil in a frying pan, sometimes folded around a filling such as cheese, vegetables, meat , or some combination of the above...

s.
An egg is fresh if it lays flat at the bottom of a glass of water. It is bad if it floats.

Different methods http://www.hormel.com/templates/knowledge/knowledge.asp?catitemid=9&id=403:

• Break the egg and use your fingers to strain out the yolk, while the whites run into the bowl below. This is very quick but messy.
• Crack the egg in half and cradle the yolk in one half of the shell (using the other half of the shell to keep it from slipping out) while draining the white into a bowl. If some white is left with the yolk, carefully pass the yolk back and forth between halves until it is all drained, being sure not to break the yolk on the sharp edges of the shell. Then deposit the yolk into another bowl.
• Break the egg on to a plate, and trap the yolk under a glass. Carefully, drain off the whites, lifting the glass slightly.
• Use a needle to pierce the egg and run the whites out, leaving the yolk inside.
• Break the egg into a funnel
  Funnel
  A funnel is a pipe with a wide, often conical mouth and a narrow stem. It is used to channel liquid or fine-grained substances into containers with a small opening. Without a funnel, spillage would occur....
  
  , thus capturing the yolk.

Specialized tools are also available for this process.