It's a "NoSQL" key-value data store. More precisely, it is a data structure server. Not like MongoDB (which is a disk-based document store), though MongoDB could be used for similar key/value use cases. The closest analog is probably to think of Redis as Memcached, but with built-in persistence (snapshotting or journaling to disk) and more datatypes.
Those two additions may seem pretty minor, but they are what make Redis pretty incredible. Persistence to disk means you can use Redis as a real database instead of just a volatile cache. The data won't disappear when you restart, like with memcached.
The additional data types are probably even more important. Key valu...