BizTalk explained in 2 slides

Different services inside a company work with their own applications. They need to exchange information several times a day. For instance, sales people send orders to production once a day. All this correspond to non formal business processes.
Services applications must continue to be able to live their lives independently.  For instance, marketing application will be upgraded to Version 2.3 next month while other applications won't move for at least 6 months.
For these reasons, no integration between applications is done and the business processes are remain implemented at human and e-mail level.

BizTalk Server enables implementing business processes at application level. In fact, applications send and receive messages (which can be seen as machine readable e-mails). When changing or upgrading one of the applications from v2.2 to v2.3, in order to keep automated business processes working, v2.3 must just be able to send and receive messages meaning the same thing as previous version v2.2 did (format can change) to and from BizTalk Server.
People in each service just have to work with their application; they do not need to send e-mails to other services anymore. Sales people enter orders in sales application which will send a message to BizTalk. BizTalk will send the message to all applications which subscribed to new order messages. Production application is one of them.