Mickey Check was introduced to kids menus at Disneyland and Walt Disney World in 2013 to all menus - quick service and table service.
In case you aren't familiar with Disney Dining terminology, quick service restaurants are grab and go type places whereas table service is more of a traditional, sit down type of restaurant.
According to Disney Parks Blog, Mickey Check "must meet Disney Nutrition Guidelines that limit calories, saturated fat, sodium, and sugar... Kid's Complete Meals must be ordered without substitutions and include at least three of the following food groups: fruits and vegetables; low-fat dairy; whole grains or lean protein, beans, eggs and nuts."
For the full guidelines, you can check out this PDF from The Walt Disney Company here. Unfortunately, exact nutritional information of menu items is not available (more on that here), but if you order off of the Mickey Check menu, this can offer you a good foundation. At a quick glance, full meals must be 600 calories or less, but you can break it down even further if you check out the charts in the PDF.
That's all well and good... But it's a kids menu item. I can't order that, right?
Not necessarily true! While Mickey Check is a kids menu exclusive, if you're dining at a quick service location, you can order off of the kids menu... Even if no children are present. So if you're not at a table service restaurant, feel free to save yourself some calories and some money by ordering off of the kids menu, especially if you get something with a Mickey Check next to it.
To know if a menu item is a Mickey Check meal, it will have a little Mickey Mouse head silhouette with a check mark in the center of it next to the name of the menu item.