Digital Ocean as a cloud provider: What, Why, How

Details

In 2013 DigitalOcean surpassed Amazon to become the fastest growing cloud provider. What makes it so successful?
It's simple UI and minimalistic approach, great features & performance, comprehensive documentation, affordable pricing and enormous community & Ecosystem support.
Let's learn first hand:

What is it, Why to use it, DO vs AWS, use cases / best practices... which will actually lead us to the docker kind of discussion / trends.