1A formal, polite greeting used when leaving — the humble (kenjōgo) version of 行ってきます, formed by replacing the auxiliary verb くる with its humble form まいる. Used in workplaces, with clients, with in-laws, in public/official settings, and other contexts requiring extra respect. Considerably more formal in tone than the everyday 行ってきます used at home. In modern writing the まいる portion is usually written in kana.
それでは取引先に行ってまいります。
Well then, I'll be heading out to the client now.
お義母さん、ちょっと買い物に行ってまいります。
Mother (mother-in-law), I'll just pop out for some shopping.
来週から一週間、出張で大阪に行ってまいります。
Starting next week I'll be away on a business trip to Osaka for a week.
ご挨拶に行ってまいりますので、お先に失礼いたします。
I'll be heading out to pay my respects, so please excuse me first.