Mars is how you go after things: drive, desire, anger and the way you fight. In Virgo, the sign ruled by Mercury and built for precision, that drive runs through a very specific channel. You work through the problem the way others avoid it: by noticing every flaw, fixing it, and finding three more. The motivation is usefulness, rather than ambition in the grand sense or raw force. The question Mars in Virgo asks, before it acts, is whether the thing will actually work.
Virgo is an earth sign and a mutable sign. The earth keeps Mars grounded and practical; the mutability keeps it adaptable, willing to change tack when new information comes in. Mars has no special dignity or difficulty in Virgo, no rulership or fall, so it works steadily rather than brilliantly or badly. Steady, in this case, means a lot.