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And I don't mean stain removers, but literally tap water.
See here's the thing, you can't remove a stain without some sort of friction, and water reduces friction. Yet if I say, spill some coffee and later remove the coffee stain, if I were to wipe it with a cloth, very little happens. If I wet the cloth, it's stupidly easier.
As @Tweej suggests, it's because of water solubility. Because water molecules are quite polar, most things that are charged or polar are soluble in it (i.e.~"hydrophilic"). When a coffee stain dries up, the residue sticks to the surface. But when water is applied, it will readily mix with the water, and more easily be removed.
Fats and oils are hydrophobic, and tend to separate from water --- which is why oil stains are so much harder to remove (with water, and water-based cleaners).
