How to explain devops to non-techy managers?
Being a consultant I am contractually obliged to answer, "it depends".  With that out of the way, I can actually answer your question.

What does it depend on? Well, that could come down to what your boss thinks about DevOps:


If your boss has heard of the term, via their obsession with CIO.com maybe, then ask them what they think it means.  From there work out what the difference is and if their view is compatible.  Identify a suitable project to trial DevOps on and pitch it to them.  Remember that at the core DevOps is culture so consider how that could be applied to a project. 
If your boss has never heard of the term then build a business case for DevOps. Use the Puppet Labs State of DevOps and material from books such as The Phoenix Project to write the business case.  Find a problem that your boss has and DevOps could solve and use it as a conversation starter. As kenchew said you don't have to mention DevOps, you might for example, suggest that Operations be more involved in a project or more test automation to be planned as part of project delivery.
If your boss thinks DevOps is just another buzz word then do one of the above but absolutely don't mention DevOps, look at other similar models such as Site Reliability Engineering, Platform Engineering or Continuous Deployment and find out how they could solve the problem.


The key is to focus on understanding what your boss is motivated by, then carve out a small bit of time, money and people to take tangible steps to solving that problem.

I highly recommend the book To Sell Is Human by Daniel H. Pink, fundamentally Daniel Pink talks about how selling something is a very human thing to do, all we need to do is tap into the needs and align our "pitch" by proposing a solution that serves those needs.