A fleece is a sheep's coat. Or a goat's. Or a yak's. A person's coat can be called a fleece, too, if it comes from a sheep or goat or a yak or even if it just looks like it did.
You can also use fleece in an informal way to mean cheating someone. Remember how Mary had a little lamb whose fleece was white as snow? Well, it was such a nice, clean fleece that Mary tricked the lamb into trusting her, then robbed him of his fleece and turned it into a bomber jacket and a pair of boots. She totally fleeced him!
Primary Meanings of fleece
outer coat of especially sheep and yaks
shear the wool from
a soft bulky fabric with deep pile; used chiefly for clothing
rip off; ask an unreasonable price
n outer coat of especially sheep and yaks
n tanned skin of a sheep with the fleece left on; used for clothing
v rip off; ask an unreasonable price
charge (someone) too little money
extort, gouge, rack, squeeze, wring
obtain by coercion or intimidation
get or extort (money or other possessions) from someone