In Active Directory, a tree is collection of domains that allows for resource sharing across the domains. For domains to be joined into a tree, they must have contiguous namespaces. In a tree, there is a Kerberos-style transitive trust relationship between the domains.
To establish resource sharing between domains with non-contiguous (that is, disjointed) namespaces, a forest is required. All trees and domains in a forest share the same schema and same global catalog. Likewise, there is a transitive trust relationship between all domains in a forest.