It would be hard to describe.

It's a low boiling point oxygenated hydrocarbon solvent, so it smells like you'd expect - think things like rubbing alcohol, ethanol (vodka), paint thinner (the ones that have alcohols in them).

Diethyl ether smells very "heavy", for lack of a better word, and pungent. It's almost overpowering, and can become unpleasant after a while.

Tetrahydrofuran (which is just diethyl ether with both ends of the ethyl groups bonded to form a ring) has a "lighter" smell, isn't overpowering and smells "clean" to me. It's still a oxygenated solvent, so it's not pleasant like the smell of flowers or spices, but to me it's more similar to ethanol which is relatively pleasant.