"What, not how" is a software development approach that emphasizes what a product will do, rather than how it does it. This way of thinking has its roots in business rules but is commonly being transferred to software development with great effect.
Business rules are a way to (digitally or otherwise) automate a decision so that there is no debate or uncertainty about what to do when a decision needs to be made.
A simple example of this is when someone chooses to wear the same outfit every day of the week, as Steve Jobs or Barack Obama have been known to do. Rather than having to decide what they're going to wear, they've created a rule that automates this daily decision. In a business context, this is used for making decisions at various points in a business's workflow.
“What, now how” applies the same logic to software design. Rather than describing how an application is going to work — which quickly becomes complicated for anyone who isn't a developer — you describe what the application is going to do, what it needs to work, what it will do in case of an error, what it expects of users, and so on.
This provides a better framework for envisioning and explaining a software project and is much more useful when you sit down to start writing an application. By considering the "what" of your project up front, you have fewer decisions to make during development, speeding up the planning and development phases.