Power indicates force of will, the higher the POW, the higher the aptitude for magic. Power does not quantify leadership, which is a matter for roleplaying. THe amount of Power or the number of magic points (they derive from Power) measure resistance to magical or hypnotic attack. An investigator without POW is zombie-like and unable to use magic. Unless stated otherwise, lost POW is lost permanently.
POW x5 is the Luck roll, about which see further below. The amount also equals a character’s initial SAN characteristic. Magic points, unlike Power, are spent and regenerated. The POW of ordinary characters rarely changes. One who is adroit in the magic of the Cthulhu Mythos may be able to increase personal POW. See How Sorcerers Get That Way.