In regard to phones, this usually refers to MIL-STD 810, which is the US Military's set of requirements for rugged devices that must endure specific environmental conditions encountered in the field. Therefore a phone advertised as adhering to MIL-STD 810 has been designed and tested to withstand the elements in one or more specific ways.
MIL-STD 810 contains many sub-categories for different extreme conditions. Few devices support them all, so it is important to note which specific categories within 810 a device is rated to withstand. For example, a device rated for shock might not be rated to withstand rain.
The military periodically revises the spec. Version 810F was in effect from 2000-2008. In late 2008, it was replaced by 810G. For most consumer applications, the revision is not very important.