A profile completion score shows how much details about your business you have added to your business page. This is shown when you log into your business dashboard. The score is shown in percentage.
You can improve your profile completion score by updating additional information like photos of the business, what features your business offers such as free parking, free wifi, and social media links. All these additional information can be updated from the Maintain Profile link on the dashboard
To get a fair idea of how this score is computed, click on the profile completion score or on view details next to profile strength in the business dashboard. You should get details like those in the image below. This way you know what details to improve on to better your profile completion score.