Water was coming out of my bathroom faucet slowly, so I removed the faucet head to clean it out and there was this thin rubber disk inside. The faucet is working fine with it removed.
if it is part of the washer for one of the valves under your sink
if you had to fix or replace something on you faucet it maybe had to shut off the hot or col valve or it may not shut off at all.
so its not an emergency but you would want to fix it.....