Each restaurant and a cafe is inspected by an organization called the New York City Department of Health and Mental Hygiene, and every restaurant and cafe is obliged to display the assessment of hygiene at the entrance, in a place visible to everyone who enters it.
“A” is the highest grade, “B” is good. However, “B” means that something did not allow this place to get an “A’” and not only the restaurant owner, but also diners understand this and it is likely they will go and search for an “A’ restaurant. Therefore, the owner will do everything possible to get a cherished sign with the letter “A”. “C” - these are very rarely seen, maybe because it is unlikely that anyone will ever want to visit a place like that.
Often you can see another sign, "Grade Pending". This means the place is being re-evaluated, or the owner is in the process of disputing the inspection’s decision. If you would like to get more information, there is a website where you can see an assessment and a detailed report for each restaurant.