say you are on MACHINE1, and it belongs to DOMAIN1.
Now, if DOMIAN1 trusts DOMAIN2, then when you sit down to MACHINE1 and press CTRL+ALT+DEL, in the Domain drop-down list, there are 3 choices, DOMIAN1, DOMAIN2 and the local machine MACHINE1.
You see, for every domain that your domain trusts, that domain is then listed in the Domain drop-down. The idea here is that any user from any trusted domain can log into any machine that is a member of any of the trusted domain, and log in using their domain username/password/domain.
So, users from DOMAIN2 can come into the office of DOMAIN1, sit down at MACHINE1, and log into DOMAIN2 with their username and password, just like when they are in THEIR OWN office.
I know, a lot of "domain this" and "domain that" but that is how it works. :-)