Short answer
A double-yolk egg forms when two yolks are released close together and travel through the oviduct within the same set of white, membranes and shell. It is especially common in young hens with irregular laying cycles.
A timing variation, not twins in the usual sense
The hen’s ovary releases two yolks before the previous one has moved far enough through the reproductive tract. Both become enclosed in one egg. Double yolks can occur in older hens too, but young flocks often produce clusters of them.
Nutrition follows edible size
A double-yolk egg is often larger and contains more yolk than a standard egg, so it generally supplies more energy, fat, dietary cholesterol and yolk micronutrients. It should not be counted as nutritionally identical to one ordinary large egg.
Cooking and baking
For frying or boiling, allow for the larger size and thicker centre. In precise baking, weigh the out-of-shell egg because an extra yolk changes fat, water and emulsification. Commercial double-yolk cartons are selected by size or scanning rather than produced by a special recipe.