As mentioned elsewhere on this thread, you'd use Swift (and other object storage systems) to store larger pieces of unstructured binary data (eg. images/videos/backups). The easiest way to do that in Cassandra without rolling a whole bunch of new code for yourself would be to store these things as gigantic rows in Cassandra, which isn't where it performs well. Typically object storage systems also come with a whole lot of features such as being able to control who views your files, the ability to upload files in piecemeal fashion, etc.
Swift is part of the larger family of OpenStack. Swift should provide (haven't verified this myself) better integration with all of the other OpenStack components (Keystone, Cinder, Neutron, etc.).
Swift can integrate with OpenStack, but you can very easily run it stand alone, and many do. It has erasure coding, geo replication, and its a fairly well baked product.
Are there use cases where Swift is a better fit than Cassandra?