"A spiced aromatic liquor or stock used mainly for cooking fish and shellfish... "
Larousse Gastronomique (2001)
That's what it is. In the same way you might call an oxtail stew a "slow-cook", a court bouillon could be translated as a "short-simmer". It's just a gentle infusion of a few aromatic flavourings into water to create a lightly-perfumed poaching liquor.
What I have found to be a source of frustration is that you generally either come across recipes in which you are instructed to make the specific quantity of court bouillon that applies to that particular recipe, or you find a recipe in the back of a cookbook for a quantity way in excess of that which you need for a small meal. So I set about trying to devise a formula that could easily be used to make court bouillon in the quantity required for a meal that you have in mind at a given point in time. After a bit of research among my cookbooks I have settled on this as a basic workhorse formula and it's derived from "Rick Stein's Seafood".
This uses a basic minimum selection of ingredients to create an all-purpose court bouillon in the quantity of 1 litre. For each additional litre or part thereof, simply multiply up the ingredient quantities. Depending on the dish being prepared, additional flavourings may be desirable, and I have listed several of the most common ones.
It is important to completely submerge the fish with liquid when poaching. The simplest way to know how much liquid is required is to put the fish in the dish in which it is to be poached and, using a measuring jug, measure the quantity of cold water required to cover the fish. This, then, should be the quantity of water upon which to calculate ingredient quantities for your court bouillon.
Ingredients (per litre of water)
1 litre water
1 small onion, sliced
1 small carrot, peeled or scrubbed, sliced
1 large or 2 small fresh bay leaves (dried are fine)
6-10 black peppercorns
1½ tsp white wine vinegar
1 tsp salt
Vegetables etc.: leek, fennel, celery, lemon slices, ...
Acids: white wine, lemon juice, ...
Herbs: parsley, thyme, ...
Spices: star anise, coriander seeds, fennel seeds, pink peppercorns, ...
Put all the ingredients into a saucepan or the vessel in which the fish is going to be poached. Bring to the boil then reduce the heat and simmer very gently for 20 minutes. The court bouillon is now ready to use.
For a more intense flavour the court bouillon can be left to cool with the ingredients still within.
The court bouillon can be used as is, or strained into the poaching vessel. The latter approach makes it easier to avoid inadvertently collecting the flavouring ingredients when lifting the fish from the liquid.
Sieved court bouillon can, of course, be frozen, but it's so quick and easy to make it's hardly worth taking up the space in the freezer.
"Larousse Gastronomique", Joël Robuchon et. al. (2001), pp. 352: https://www.amazon.co.uk/Larousse-Gastronomique-Hamlyn/dp/0600620425
"Rick Stein's Seafood", Rick Stein (2001), pp.223: https://www.amazon.co.uk/Rick-Steins-Seafood-Stein/dp/056349347X