I think there were multiple reasons why containers started to gain traction. If you ask 3 people why they started using containers, you're likely to get 4 answers.
For me, it was avoiding dependencies and making it easier to deploy programs (not services) to different servers w/o needing to install dependencies.
I seem to remember a meetup in SF around 2013 where Docker (was it still dotCloud back then?) was describing a primary use-case was easier deployment of services.
I'm sure for someone else, it was deployment/coordination of related services.