The small hole near most bathroom sink faucets is an overflow hole designed to prevent flooding. If the water level gets too high, it drains through this hole to avoid spilling onto the floor.
However, it can accumulate bacteria and mold, causing unpleasant odors. To clean it, mix vinegar and baking soda, pour it into the hole, and let it sit for 5–10 minutes before flushing with warm water to keep the sink fresh.