It's an illustration by sci-fi artist David Mattingly(the illustration above is the same one as in my signature, but larger...) of sci-fi heroine Honor Harrington and her treecat Nimitz. Harrington is the main character in David Weber's Honorverse series of military sci-fi novels and anthologies. Her character is based off of three individuals(2 real-life and 1 fictional); Admiral Horatio Lord Nelson and Admiral Thomas Cochrane, along with C.S. Forester's fictional character of Horatio Hornblower.
As to the illustration....I thought it looked pretty interesting, so I thought I'd add it to my signature.