Base64 is a method of encoding binary data into a form of pure text that can be (for example) safely e-mailed. It is intended to be the mechanism for encoding file attatchments to e-mail using MIME, and is generally thought of (coupled with MIME) as a newer alternative to uuencode. Its internal workings are described in detail in part 5.2 of RFC 1521.

Most modern mail clients will transparently encode and decode base64, so you don't really need to be aware of the fact it exists.