You can set up hosted git in a few hours. What is the use case of GitHub?
You can set up a server in a few hours. What is the use case of Heroku?
So the first use case of Circle is that you can set it up in seconds. Literally, 20 seconds. You spent a few hours setting up your CI servers, but what if you didn't have a server available, didn't know how to set up postgres, couldn't put a hole in your firewall for the github notifications, or forget to add "bundle exec" to your rspec calls?
Aha you think - I'll use EC2. So you rent a server (for the same cost as Circle), set up Jenkins, but somehow your tests keep failing. But only sometimes. Why is that? It's because EC2 has such ridiculously bad IO that your integration tests time out while logging into the server.
OK, so solve that problem, then your organization grows to 5 people, and your test suite to 5 minutes. You all push code one day, and now have to wait 25 minutes to get test results.
Then tests grow to 20 minutes, and the team to 12. Now you're in a deep hole, and you're bringing up servers as fast a you can, trying to remember how to configure them the same, and of course you've moved to a different project so it's actually your coworker doing it, and he doesn't know what you did.
We solve every problem here - easy to set up, incredibly fast, auto-scaling, and we can even parallelize your builds so that a 60 minute test suite on your machines runs across 4 machines and takes 13 minutes.
And Circle (again, at https://circleci.com) won't go down if you go on vacation.