Exchange server uses the JET database engine to store its data. JET is the same engine which Microsoft Access uses, only this is a much larger and more powerful version of it.
Basically all databases store their data in a tabular format. There are rows and columns. In Exchange the columns are simply named things like MessageId, To, From, CC, BCC, DateSend, DateReceived, Headers, Subject, Message, Attachments, etc.
Which version of Exchange are you asking about? This has changed between versions slightly.