Definition of big heads:
(n) :
(idiomatic) An inflated ego, an exaggerated belief in one's own importance.
(n) :
(idiomatic, usually humorous) The brain, as opposed to the penis, little head; rational thought, as opposed to lust.
(n) :
(figurative, sometimes capitalized) The short head of a long tail distribution.
(n) :
Alternative form of bighead (“person with an inflated opinion of themselves”). [(countable, colloquial, especially used by children) A person with an inflated opinion of themselves; a conceited or arrogant person.]