"Direct" is short for the secure exchange protocol developed by HHS Office of the National Coordinator (ONC) "the Direct Project". The basic idea was to make secure exchange of electronic health records as easy as sending by fax... and in many ways, Direct has accomplished this goal.
Direct messaging is embedded in most EHRs and and can be used in messaging, referrals or transitions of care. Each system may have their own user interface for using Direct messaging.
Direct messaging acts similar to email, but don't mistake it for normal email. Even though an address may look like normal email (e.g. Dr.X@direct.hispdirect.com), you cannot use Direct to send messages to or from normal email. Direct messaging is highly secure and requires identity proofing, digital certificates, and a trusted network. You can only send Direct messages to other users with a Direct address.
To find a providers Direct address, you can look them up in a Direct provider directory, or as you would with fax, ask them: "What is your Direct address?". If someone says they are using "secure email" or "HIPAA compliant" email -- it doesn't mean it's a Direct address.
NOTE: Direct is referenced as "Applicability Statement for Secure Health Transport" in the Meaningful Use Stage 2 rule. An technical overview of the project can be found on at the HealthIT.gov site.