human909 said:
Performance-based design is a design that might not directly follow the specific code requirements, but can be shown to perform equally or better than the code requirements in achieving the relevant goal.
I think Human909's answer is the most accurate one. So, he gets a star from me.
I might elaborate on it a little though as it concerns civil / structural engineering:
Design following the code can be described like baking following a recipe. Use the ingredients in the way the recipe dictates and you will end up cooking an acceptably safe structure. If the structure doesn't perform well, the baker will point to the recipe and say, "the fault is in the recipe, you shouldn't blame me."
However, a good baker, who understands all the ingredients and how they react with each other can create his own recipe for a particular purpose and expect it lead to a sufficiently safe structure. But, if the structure doesn't perform well, the baker must take the blame because he didn't use a recipe.
Performance based design allows for a more "1st principles" kind of design where you do not follow specific code provisions. But, where you evaluate an existing building for safety using more advanced criteria and analysis such that the building can be proven safe. Sometimes this means retrofitting the building to behave with more ductility to prevent anticipated non-ductile failure modes. Or, it may merely demonstrate that the ductility provided by the existing building is sufficiently safe for occupation without upgrade.