see also Soaping
The soap brush is used to apply saddle soap to leather. Ideally the bristles should be soft to medium hardness. Stiff bristles are useful when dealing with sticky, oily, or particularly caked dirt, but for general purpose grime, softer bristles cover the leather better and produce a better foam.
A common soap brush is the so-called "Pro dauber", a large (approximately 2 inch diameter) round brush with a handle projecting from the side of the brush. The bristles are soft and about 1 inch long.