This isn't necessarily Monrovia specific but you can find these letter grades on the restaurants, markets and pretty much any businesses that have food for sale. They reflect the results of periodic inspections by health inspectors from the Los Angeles County Department of Public Health. The "A" grade, of course, being best.
The inspections are required and so is the posting of the grades. The department has a website that allows you to search many different ways (business name, city, etc.) to find not only the score of any businesses you're interested in but also any problems that may have been found.
For Monrovia, out of 179 businesses listed, 164 had an "A" rating and only 1 had a rating below a "B". Great job!