A muffle kiln is typically smaller than a conventional glass or ceramic kiln and has a lower maximum temperature. The primary use is to fire paints, enamels, gildings and lusters.
Merriam-Webster Online defines muffle as meaning to wrap up so as to conceal or protect. Muffle kilns typically had an interior chamber or box (the muffle) that protected the delicate paints and gildings from direct exposure to the kiln's flames.