Answer: CARPETS

Carpets are floor coverings that are typically made from woven fabric or other materials. They are used to cover the floors of rooms and provide a soft surface for walking or sitting. Carpets have the ability to absorb sound and minimize noise, which is why they are often associated with quieting one's footsteps.

Note: The provided meaning of the answer is for the latest New York Times crossword puzzle clue: They quiet one's footsteps. Explanations are generated by AI and may be inaccurate.