Comes from "Military Specification/Standard". With regards to mobile phones, it normally refers to the US Army's set of standards, called MIL-STD 810.
These standards specify the requirements that a rugged device must fulfill, such as surviving certain environmental conditions.
There are lots of sub-categories of the MIL-STD 810 referring to different extreme conditions. As only a few devices support all sub-categories, it is important to note exactly which of them is supported by a certain device. A capital letter added to the name indicates which specifications are met - MIL-STD 810F for example means resistance to rain, shock, vibration, dust, humidity, salt fog and extreme temperatures.