Swift is the Openstack project for object storage. Object Storage in general (and swift specifically) provides large scale, cheap, and durable storage. Swift is not used like a traditional hard drive - Object storage is all about relaxing some of the constraints of a POSIX-style file system. The access to it is API-based (and the API uses http). This is a good idea as if you don't have to provide atomic operations (ie you can rely on eventual consistency), you can much more easily scale a storage system and avoid a central point of failure.

nova-volume and Cinder are for block storage attached to a virtual machine. Where Swift isn't a filesystm, nova-volume is - designed to provide "mountable" devices.