also: もてき
noun
period of romantic popularity
Colloquial term for a phase in life when one suddenly receives more romantic attention than usual. Often used humorously or self-deprecatingly.
See also: モテる
大学生のとき、突然モテ期が来た。
When I was in college, I suddenly had a period of romantic popularity.
彼は今モテ期らしくて、毎日デートの誘いがあるそうだ。
He seems to be in a popular phase now, and I hear he gets asked out every day.
モテる is the verb meaning 'to be popular (romantically)'; モテ期 is the noun for the period when that happens.
From モテる (to be romantically popular) + 期 (period). The exact origin is uncertain, but it likely arose in colloquial speech.