Definitions from Wiktionary (big head)

▸ noun:  (idiomatic) An inflated ego, an exaggerated belief in one's own importance.
▸ noun:  (idiomatic, usually humorous) The brain, as opposed to the penis, little head; rational thought, as opposed to lust.
▸ noun:  (figurative, sometimes capitalized) The short head of a long tail distribution.
▸ noun:  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.]

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