To do something without making any noise.
Doing something soundlessly can be sneaky or careful.
Examples:
The cat walked soundlessly across the room.
She opened the door soundlessly so she wouldn't wake anyone up.
He moved soundlessly through the forest, trying not to scare the animals.
The ninja moved soundlessly through the night, like a ghost.
The ghost glided soundlessly through the walls.
The snow fell soundlessly outside, covering everything in white.