Not to be confused with the more general Museum Day in September, which is sponsored by Smithsonian magazine (my post here), Art Museum Day is a relatively new event, started last year, that is sponsored by the Association of Art Museum Directors.
This Saturday, May 18, 2013, participating art museums in the U.S. Canada and Mexico will be offering free or reduced admission, special programs and other events in a bid to attract additional visitors.
The page on the AAMD site lists participating museums, with some indication of specific events, though you should probably check with your local museum in question for more specifics. There is also an AAMD press release about the event, with a more compact list of the museums, here.
The event is held in on the same day as International Museum Day, which features events at museums in Africa, Asia, Europe, Oceana and the Americas (look to links on the right of the IMD page for more information about museums and events in specific world regions).
(Above: images of a few participating art museums in my area: The Philadelphia Museum of Art, The Brandywine River Museum, The Pennsylvania Academy of the Fine Arts Museum of American Art, The Delaware Art Museum)