AppleSingle is similar in concept to the more popular MacBinary format, in that the resource and data forks are combined together with a header containing the Finder information. In fact, the format is so similar there is no obvious reason why Apple did not simply use MacBinary instead, which by that point was widely known and used. The format was later assigned the MIME type application/applefile.
AppleDouble leaves the data fork in its original format, allowing it to be edited by normal Unix utilities. The resource fork and Finder information, both "private" and lacking editors under Unix, were combined into a second file. A MIME type was also assigned to AppleDouble, multipart/appledouble. For sending to an AppleDouble un-aware system, the file was generally encoded using Base64, as opposed to being converted to AppleSingle.
Before Mac OS X, AppleSingle and Double had little presence in the Mac market, due largely to the small market share of A/UX. Nevertheless they did force various file compression vendors to add support for the formats, and confuse future MacBinary versions.
Mac OS X revived the use of AppleDouble; on file systems such as NFS and WebDAV that don't natively support resource forks, Finder information, or extended attributes, that information is stored in AppleDouble format, with the second file having a name generated by prepending "._" to the name of the first file (thus, this information acts a hidden file when viewed from a non-apple Unix-based operating system).