This phrase was told to me by my father
who is a Colonel
(Ret.) in the US Army
. Essentially it means don't do anything to stand out. Don't be taller, thinner, shorter, fatter, louder, smarter or more visible than those around you. Excellence is a good way to have the higher authority know your name. This can apply to work, school and life in general.
Oh, and never volunteer for ANYTHING!
Update: This idea is illustrated in Kubrick's Full Metal Jacket. In one scene the Drill Instructor goes off on a recruit; at one point he yells "I know your name!"