Bathroom sink drainage
When you plunge a sink with an overflow built into it you must first plug the opening with a plastic bag so a vacuum is created.
The overflow and the drain are connected when the sink is designed. Sometimes if plunging won't open the drain removing the trap and checking for obstructions is best.
If the clog isn't in the trap by removing it you can than peer down the drain from above at the sink. The stopper lever is also a location that is notorious for causing clogs.
Lastly, if you verify there are no clogs along the exposed drain line and plunging doesn't help, an augured drain snake pushed into the pipe gong into the wall may be your last hope.
I don't recommend any type of clog dissolver or acidic solutions to open the drain as they can do more harm to the pipes and septic system than good.