male presence; masculine aura
Often used in negative expressions like 男っ気がない to describe a man who lacks a masculine vibe or a place without men around. Can also refer to a man's attractiveness or ruggedness.
He's kind, but I feel he lacks a masculine presence.
This workplace is all women and has no male presence.
Compound of 男 (おとこ, 'man') + っ気 (っけ, a suffix indicating a sign or presence). The suffix っ気 is a colloquial variant of 気 (け, 'sign, feeling').