Let's start with the definition of "engineering analysis"

Engineering analysis involves the application of scientific analytic principles and processes to reveal the properties and state of a system.

It breaks the system into it's components parts, analyzes those parts individually and then synthesizes those components based on physical principles and natural laws. 

So health and performance engineering is looking at all the individual components that collectively comprise optimal health (nutrition, fitness, stress, recovery, sleep, and even the mental and emotional aspects) through comprehensive analysis and assessment and then creating an individualized plan that accounts for all the variables and maximizes results within the time frame available.

Health and Performance Engineering is taking the cogs of our lives, typically viewed as separate entities or pieces, and putting them together into a fully functional whole.