Bouillon comes from bouillir, ‘to boil’; it’s also the word first used in the mid 19th century for a kind of affordable restaurant, a bit like a soup kitchen. It was around then too that Justus von Liebig came up with a process to manufacture meat extracts and eventually the instant stock cube.
As elsewhere, the French make good use of bouillon cubes, as well as powdery fond de veau and fond de volaille.
If you’re following a recipe, you may see:
chauffer à gros bouillons: heat to rolling boil
donner un bouillon: heat until it boils
écumer au premier bouillon: skim the scum when it first comes to a boil
les yeux du bouillon: fat bubbles on the surface
Image by Kui-Doraku, Creative Commons License