Although this may sound too simple, it spreads the oil throughout the liquid again and coats its beads with emulsifiers, fixing the vinaigrette without affecting the flavors.
Emulsifiers like honey, mustard, and mayonnaise unite oil and water, encasing themselves around the liquids and acting as a barrier that doesn't allow the molecules to repel.
You could also throw your dressing in a blender for a quick fix, but the intense speed will be too harsh on the oil and create oxidization, leading to a bitter-tasting vinaigrette.