Amazon S3 is basically a hard drive in the cloud with similar functionality to Dropbox, Google Drive, and SkyDrive. The biggest difference is that Amazon S3 has more functionality, but it's also more difficult to use.
Amazon S3 and WordPress can work together to embed videos in your website. You can also protect those videos using special settings in your S3 account. The other cloud storage services don't have those abilities.
There is a cost associated with Amazon S3, but it's really cheap. You can see the pricing on this page: