By inserting the hand, cupped, into the bell, the player can reduce the pitch of a note by a semitone or more.
This, combined with the use of crooks changing the key of the instrument, allowed composers to write fully chromatic music for the horn and almost fully chromatic music for the trumpet before the invention of piston and valve horns and trumpets in the early 19th Century.
Some pieces call for notes to be played stopped (sometimes written as gestopft in the score) specifically in order to produce this muted tone.
As the palm closes the bell, the effective tube length is increased, lowering the pitch (up to about a semitone for horns in the range D through G).
But when the hand stops the bell completely, the tube length is shortened, raising pitch about a semitone for horns tuned near to the key of F.