The adjective primal describes something that's essential or basic, like the primal urge to protect yourself and your family from harm.
The Latin root of primal is primus, which means first. If your friend talks about his primal self, he means the most basic, important part of who he is. You can think of this as a first priority, just as the primal urges of all animals is survival. Primal can also describe something that's original, or at its earliest stage, like a primal or primeval forest, the most ancient example of that kind of terrain.