edit: I have not used containers with amazon web services but it is really nice to have on my VPS as virtualization and even paravirtualization are not typically an option.
It's also very useful in deployment, I have different containers for my web, primary worker and mongo replicasets. Combined with Digital Ocean it makes it very easy for me to quickly spin up new servers and set them up as needed with only a few commands. There is also comfort in the fact knowing that I can do the exact same thing on linode without any modification to the container.
For a single application, docker doesn't add much except for portability. For a single application with many components, docker adds process isolation (and quotas, and ...).