"a cloud hosted database" + "run arbitrary JS in response to events at scale" covers most of it. It's a hosted database and server.
Parse was a:
* cloud hosted nosql database,
* with client libraries for mobile platforms,
* direct write access from mobile apps, without hosting your own API backend in the middle, and
* some methods of securing this direct write access from untrusted clients.
Other important parts may include "runs on node.js", "server code in JS", "client + server define ACL per row", "push notifications", "amazingly, supports windows mobile", etc, depending on the viewer. That's what the rest of the documentation is for, e.g. in a features list.