There are two features which make the Sony MiniDisc uniquely different from both CDs and tape.
First, it uses ATRAC compression. Using the same basic techniques as MP3 compression, ATRAC removes the frequencies most people wouldn't hear anyways and then compresses the rest. This is what makes it possible to record a whole CD worth of music in one-quarter the space. However, it also ensures that MiniDiscs will never be a replacement for CDs or DAT so long as some people want or need high-quality, uncompressed audio.
Second, it uses a table of contents. This is an advantage over both CDs and tape because it lets the owner edit a MiniDisc quickly without re-recording. Want to delete a track in the middle of your mix? It's gone in a second. Want to rearrange the order of your tracks? That's just as easily done. Once the music is recorded on the MiniDisc, it can be reorganized and rearranged just as easily as the directories on your computer's hard drive.