Kodiak refers to an island in Alaska. As such it is used in branding to convey a feeling of the outdoors, the life of a woodsman, a tough guy, or the Alaska lifestyle, perhaps conjuring images of Jack London's writings (such as in the aforementioned tobacco, but also in the restaurant chain "Kodiak Jack's" etc. So, in the usage above it might be trying to suggest that the chewer of that particular brand is that kind of guy.

Its a a brand of smokeless tobacco that is strong. It is a type of moist snuff or dipping tobacco. It is a common brand. Wintergreen, Mint (formerly Ice), and Straight are some of the kinds of flavor for Kodiak. -Like Marlboro has lights, reds, etc.