From the marketing glossy it would seem they use public key crypto, with two authentications stores. One is on the key and the second is on the Web.
The key is used to authenticate you to the TriCipher key vault on the web. TriCipher then authenticates you to the financial web site. My guess is that you establish an SSL tunnel to TriCipher using a certificate on the key. You then authenticate yourself to TriCipher using something you know. Then TriCipher somehow authenticates you to the bank and establishes an SSL session between you and the bank that is already authenticated.
My guess is that TriCipher starts as a man-in-the-middle and then somehow hands off the session, maybe a reverse tunnel is established from the bank back to you?
Since you're running software off of the key and your authentication to TriCipher involves a cert and something you know, it's possible to evade key loggers. One method would be for TriCypher to display a captcha image back to the user which the user combines with their pass-phrase to create a one-time key for the session.
But this is all guess work from a marketing glossy. Might be fun to try it out.