This is from Moby Dick. Stubb is thinking this to himself. "It" is the gold doubloon which Ahab has nailed to the mainmast and promised as a reward to whoever kills Moby Dick.

This means that the "old Mogul" has been looking at the coin, with a suggestion of looking in a sly or surreptitious way.

If we look at the 1913 revised Webster dictionary, we see that "twig" could mean "understand", as it can colloquially nowadays, but also:

"1. To understand the meaning of; to comprehend; as, do you twig me? [Colloq.] Marryat.
2. To observe slyly; also, to perceive; to discover. Now twig him; now mind him." Foote.
As if he were looking right into your eyes and twigged something there which you had half a mind to conceal. Hawthorne."
http://machaut.uchicago.edu/?resource=Webster's&word=twig&us...

The possible element of observing it slyly may reflect the fact that the crew are rivals for the doubloon, so they don't want to look at it in too obvious a way.