It's an in-memory hash store that is persisted to the disk when possible. Sort of like memcached that can survive restarts and is suitable for long-term storage.
Ah OK. I believe redis persists automatically when it can, from the memory, though I haven't actually used it. With a MySQL memory table, if you want to write to the memory table AND have it persist, you have to keep track of what has changed yourself, and handle writing those things to disk.