A polite set phrase said when leaving home or a place, implying you will return. The typical response is いってらっしゃい.
See also: いってらっしゃい
「行ってきます！」「行ってらっしゃい。」
"I'm off!" "See you later."
学校に行ってきます。
I'm off to school.
行ってきます is said when leaving home, while ただいま is said upon returning, making them opposite halves of the same daily routine.
行ってきます is the everyday phrase for leaving home, while 行ってまいります uses the humble verb 参ります to sound more formal and polite.
Standard kanji-kana spelling; the most common written form.
Alternate spelling using the kanji 来; also common.
From the te-form of 行く (iku, 'to go') + 来る (kuru, 'to come') in polite form, literally 'I go and come back'.