The relevant meaning of muffle to understand what is muffle furnace.
(v. t.) A small oven for baking and fixing the colors of painted or printed pottery, without exposing the pottery to the flames of the furnace or kiln.
(v. t.) An earthenware compartment or oven, often shaped like a half cylinder, used in furnaces to protect objects heated from the direct action of the fire, as in scorification of ores, cupellation of ore buttons, etc.
A muffle furnace is a (usually) front-loading box-type oven or kiln
for high-temperature applications (up to 1200 C) such as fusing glass,
creating enamel coatings, etc.