Ask HN: Why use Docker and what are the business cases for using it?

I recently did a very basic tutorial on Docker. Afterward, when talking to the tech lead of the project I am working on, he asked me "What are the business cases for using Docker, how could it save us money, how could it make us more efficient?" I told him I would do some research to find the best answers and figured I would turn to you all here at HackerNews for some advice.

Thanks in advance!

Just so you know, I currently work on a project at my company that uses AWS, Codeship and BitBucket for development and production. AWS and Elasticbeanstalk host our application, Codeship runs tests on changes to branches in BitBucket and then pushes the code that passes on certain branches to different AWS environments for Development or Production.