Hi,
Based on my understanding ,a trust is a relationship, which you establish between domains that makes it possible for users in the domain to be authenticated by the other domain. This means if the trust relationship was created between domains(forests), users from the trusted domains can access resources from the trusting domain.
For example, there is a two way trust relationship between the Domain A and domain B. User A from the domain A. PC A from domain A ,PC B from domain B.
Then if proper permission signed to user A , when user A log into PC A, he can access the resource in domain B.
User A can even logon to the workstation PC B in domain B by using his credential from domain A (by default).On the PC B, user A \domainA.com with the user A's credential in domain A .
Best Regards,