A MailBox is a logical container for mail.

There are many different physical formats for MailBoxes, which typically use some variation on the following schemes:

A FlatFile
All the messages in a MailBox are stored in a single file. BSD's and Solaris' MBox format is the most common example.
One file per Email
MH and MailDir store each Email in a file of its own. This scales much better than the typical FlatFile format, as it is easier to skip from message to message. It is also more robust against corruption, since mishaps in any single file can only affect one message at most. The drawback is that large MailBoxes require opening a lot of files and may heavily tax your FileSystem. An attempt is often made to solve this by the use of some kind of header index/cache, but no two programs (or even versions of the same program) agree on the format they use.
A DataBase
MicrosoftExchange does this, as well as DBMail on Unix. It is often the backend of choice for WebMail systems, as well.

There are, of course, hybrid approaches, as well as various workarounds for each approach (indexing, offset tables, header cache files) to overcome the performance problems that it suffers from. Alas, all of these workarounds and differing approaches tend to be application specific, which makes the vanilla formats more practical most of the time.

For a comparasion of several different schemes, have a read of, or for an even more subjective "discussion", ;)