There is a growing body of scientific evidence that supports that their use helps stop the spread of COVID-19.
COVID-19 is spread primarily through respiratory droplets created when coughing, sneezing, and even talking. Wearing a face mask in public spaces helps stop those droplets from passing between you and others. It is not a total solution, but a complimentary one to social distancing 6 feet from one another and good hygiene such as washing your hands with soap and water regularly.
The CDC recommends that people wear a cloth face covering to cover their nose and mouth in the community settings such as grocery stores, malls, theaters, work, etc, including if they have no symptoms of COVID-19.
Note that medical masks such as N-95 respirators should be reserved for healthcare workers and other first responders.