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. Around that same time, Justus von Liebig came up with a process to manufacture meat extracts and, eventually the instant stock cube.
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