This is an expression used by military folk and their ilk
to describe the 'efficiency' of a unit, measured by the number of actual warrior
s (the 'tooth') to the number of support personnel required to keep them in the field (the 'tail'). This is not a very good measurement of much of anything involving combat effectiveness
; modern warfare, if done the high-style
way, is incredibly lethal
and consumes an enormous amount of resources, requiring more people moving the beans
than people actually putting out rounds.
As you go up the technological ladder, this ratio drops. Air forces, for example, are probably the most (in)famous examples of this, sending a very few. highly trained officers out on the effort of thousands and thousands of ground crew, supply crew, maintenance workers, yadda, yadda.
It is, of course, easy to get bogged down in what, precisely, constitutes tooth and what constitutes tail. For example, an infantry engineering battalion's role doesn't typically involve shooting at things, but building them or blowing them up. However, below a certain unit level, engineers carry rifles just like everybody else, so when it drops in the pot they can put out rounds with the best of 'em. The pejorative 'swivel-chair soldier' is usually used to identify personnel that the grunts consider to be tail (well, tail in the admin sense...that is...oh, never mind).
The extreme would be something like Robert Heinlein's Mobile Infantry from his excellent book (NOT movie) Starship Troopers. The motto of that service is 'Everybody works, everybody fights.' Although reliant on a space navy for transport, the MI sends all its personnel 'out the tube' into combat. Even there, however, they recognize the need for REMFs (Rear-Echelon MotherF------s), using civilians and disabled troopers for those jobs.
Some would say the U.S. Army of the Cold War was the worst, with officer's slots for everything in creation - morale officer, snackbar officer, make-sure-the-commander's-dog-has-a-milkbone officer.