Literally translated as adding oil on the fire, the expression means making a difficult situation even worse, exacerbating a conflict, often purposefully. It is equivalent to the English expression, adding fuel to the flames, or fanning the flames.
Note that it can also appear as jeter/verser de l’huile sur le feu (throwing/pouring oil on the fire) and that an older form puts the oil dans le feu (in the fire).
As you will likely have guessed, the expression draws upon the flammability of oil, and the idea that, instead of trying to put out the fire like any well-intentioned person would, the subject is in fact adding oil to keep the flames going.
This idiom dates back to the 17th century. In a letter to her daughter in 1673, Madame de Sévigné wrote: Vos paroles sont tranchantes, et mettent de l’huile dans le feu - Your words are sharp, and put oil in the fire.
Lors d'un conflit, il faut faire en sorte de ne pas verser d'huile sur le feu mais plutôt de calmer la situation.
In a conflict, every effort should be made not to fan the flames but rather to calm the situation down.
Déjà qu'il ne s'entend pas avec son voisin! Porter plainte ne ferait que mettre de l'huile sur le feu.
He doesn't get along with with his neighbor at all. Filing a complaint would make matters even worse!