The most ADVANCED part of our brain is the prefrontal cortext, which is sometimes called "the executive brain".
Positioned behind the forehead, the prefrontal cortex is engaged when "we do the harder thing" (as primatologist Robert Sapolsky puts it). Impulse control, delayed gratification, and choosing to act in accordance with one's higher values all depend on this most recently evolved part of the brain.
"HIGHER PORPOISE" is a playful term for this locus of our higher purpose or "higher power." Because all the great apes also have a well developed prefrontal cortex, the exceptional power of this part of the brain in humans owes to its far more massive connectivity with the rest of the brain.
This part of the brain is the top of the heap, so to speak. It is only here that conflicts within and between the more ancient parts of the brain can be resolved.
Thus, HIGHER PORPOISE is responsible for keeping in check the physical urges of our LIZARD LEGACY (Reptilian Brain) and the social drives and emotions of our FURRY LI'L MAMMAL (Old Mammalian Brain).
"Human beings are endowed by evolution with the capacity to do things that are extraordinarily independent of biology. . . People are never so human as when they act counter to some of their biologically given inclinations. This may be what truly distinguishes human beings from other animals." — David Barash and Judith Lipton (2009, Strange Bedfellows, pp. 24 & 56.)
