A .mim or .mme file is a file in the Multipurpose Internet Mail Extension (MIME) format.
MIME is a specification for the format of non-text e-mail attachments that allows the attachment to be sent over the Internet. MIME allows your mail client or Web browser to send and receive things like spreadsheets and audio, video and graphics files via Internet mail.
MIME was defined in 1992 by the Internet Engineering Task Force (IETF). The distinguishing characteristic of a MIME message is the presence of the MIME headers. As long as your mail recipients also have e-mail software that is MIME-compliant (and most e-mail software is), you can swap files containing attachments automatically.

 some tips for e-mail attachments:
You can use a utility like WinZip (PC) or StuffIt (Mac) to compress a large file before you send. Most e-mail systems will not accept messages that exceed a certain size.
It is a good idea to send attached photographs in the Joint Photographic Experts Group (JPEG) format rather than the GIF or TIFF formats. JPEG (.jpg) files use less space and therefore upload faster.
AOL and some e-mail software uses .mme or .mim files as a "wrapper" for mail that contains non-text attachments. Use care when sending a MIME attachment to users of older versions of AOL software, as the earlier versions do not handle MIME very well. Send one attachment per e-mail. If you are an AOL user, use the keyword (Ctrl+K) MIME to view help about decoding MIME files.

Base64 Encoding

To insure that email messages containing images or other non-text information will be delivered with maximum protection against corruption, MIME provides a way for non-text information to be encoded as text. This encoding is known as base64, and appears to be a source of frustration for many email users.

Decoding MIME

The transport system that moves email around the Internet can sometimes garble a message containg an attachment such as an image or audio file.

Mpack for UNIX

Not all email programs support the MIME standard, making it difficult for many email users to deal with encoded documents sent to them. The system that transports email from one computer to another is known sometimes to be unfriendly to non-text information such as images, which is why MIME includes an encoding/decoding mechanism that converts arbitrary information to text and back. This encoding mechanism is known as base64, and seems to be the source of much frustration for many email users using non-MIME compliant software. If your email software does not support the automatic decoding of base64-encoded documents, then you will need to get your hands on a utility to help you out. I highly recommend mpack. The mpack distribution actually includes two programs: mpack, for encoding images, files, etc. into base64 for sending; and munpack, for decoding images, files, etc. that have been received. mpack is available for DOS, Windows, Macintosh, UNIX, and a few other platforms. Click here for the Mpack FTP site.

From the Mpack FTP reository: mpack 1.6 is a unix only "maintenence" release. It adds no new features. Users of other platforms supported by mpack 1.5 should continue using it. The various security patches have been incorporated, as has a patch that fixes the handling of ';'s in attachment filenames

The Official MIME Specification

The definitive information on the MIME format is provided by the Internet Engineering Task Force (IETF) in the following documents:

RFC-822 Standard for the format of ARPA Internet text messages
RFC-2045 Multipurpose Internet Mail Extensions (MIME) Part One: Format of Internet Message Bodies
RFC-2046 Multipurpose Internet Mail Extensions (MIME) Part Two: Media Types
RFC-2047 Multipurpose Internet Mail Extensions (MIME) Part Three: Message Header Extensions for Non-ASCII Text
RFC-2048 Multipurpose Internet Mail Extensions (MIME) Part Four: Registration Procedures
RFC-2049 Multipurpose Internet Mail Extensions (MIME) Part Five: Conformance Criteria and Examples

MIME and the World Wide Web

The MIME format is also very similar to the format of information that is exchanged between a Web browser and the Web server it connects to. This related format is specified as part of the Hypertext Transfer Protocol (HTTP). For the definitive information on HTTP, you should consult RFC 2616 Hypertext Transfer Protocol -- HTTP/1.1.