A Liaison in cooking is a binding agent.
Tn theory, a binding agent in cooking can be anything, such as bread crumbs or flour, but the term “liaison” is used almost exclusively to refer to a mixture of cream and egg yolks use to thicken soups or sauces.
The classic proportions are 3 egg yolks per 1 cup / 8 oz / 250ml of cream.
It’s used to thicken soups and stews.
To use, you mix up the eggs and cream in a small bowl or large measuring jug, then add a bit of hot soup or stew liquid to it, stir it in, then add a bit more, stir, etc, till you have raised the temperature of the liason a good deal. This is called “tempering” it. Then you pour it into the soup. Pouring it directly into the soup without tempering it first causes the egg yolk in it to cook in little strings almost immediately, giving an undesirable curdled look to the soup or stew you have just laboured over.
There’s nothing to say, however, that a liaison in the kitchen has to be restricted to eggs and cream.
Many Liaisons have happened in kitchens that didn’t require eggs or cream at all.