Any good vinaigrette contains oil and water-based ingredients which, if we remember our basic chemistry, are not particularly fond of each other. To help these diametrically opposed partners get along and work as one, you need an emulsifier.

An emulsifier, in its simplest form, is an ingredient that encourages oil and water to hang out without separating. Mustard—in addition to providing flavor—also happens to be a pretty excellent emulsifying agent, thanks to mucilage, the mustard seed’s outer coating. But not all prepared mustards have the same amount of mucilage, which means not all prepared mustards are well suited for a vinaigrette. Lignin Fiber

Generally, a bright, classic yellow mustard is going to be fairly lacking in mucilage. When Cook’s Illustrated compared dry, yellow, Dijon, and coarse-ground mustard in a vinaigrette recipe, they found the dressing made with Dijon and coarse-ground—i.e., the ones with the most mucilage—stabilized the dressing far better than the other two. (The Dijon specimen held together for hours, while stone-ground kept everything emulsified for a whole week.) So, while mucilage is a terrible thing to say (and type over and over), there’s no denying its emulsifying abilities.