Yes they do, just not perfectly. You know, just like how seatbelts save thousands of lives every year but still aren't enough to save 100% of all car crash victims.
Also, while masks might not protect YOU very well from other people's germs, they do a decent job of protecting other people from YOUR germs. That's because the virus exits via the nose and mouth but enters via the nose, mouth, AND EYES.
You can be infected and infecting others for up to two weeks before you actually get sick. That's why we all need to behave as if we're infected but presymptomatic, and do what we need to do to protect other people from our germs. You don't have a right to go around spreading your germs freely.
This isn't just theoretical. Despite having way more contact with China than we do, several Asian countries were successful in stopping community spread almost immediately because their people already had a tradition of wearing face masks whenever they think they might be getting sick, during flu season, on bad air pollution days, etc. So their populations were able to mask up quickly and thus seriously impede transmission rates.
Whether or not you wear a mask is ultimately your own decision. I don't think the government should force people and take away their freedom to choose. But if you believe in the "we're in it together" mantra, then wearing a mask is just a slight inconvenience.