1A humble (kenjōgo) verb meaning 'to receive' — used to politely indicate receiving something from someone.
先日、先生から本をいただきました。
The other day I received a book from my teacher.
ご寄付をいただき、ありがとうございました。
Thank you for your donation.
お電話をいただき、感謝します。
Thank you for calling.
2A humble verb meaning 'to eat' or 'to drink' — used when speaking modestly about oneself receiving food or drink.
それでは、いただきます。
Well then, I'll eat (thank you for the meal).
ごちそうをいただきました。とてもおいしかったです。
Thank you for the meal. It was very delicious.
3Original/archaic meaning: to be crowned with or to wear something on the head.
王は戴冠式で王冠をいただいた。
At the coronation the king was crowned with the crown.
4To have someone as one's leader or sovereign; to live under or serve them (used in older or formal contexts).
この地方は長年にわたり名君をいただいてきた。
This region has long had a wise ruler.
5An auxiliary verb attached to the -te form indicating receiving the favor of someone doing something ('to have someone do ~' politely); common in requests and polite expressions.
説明していただけますか？
Could you explain it to me?
手伝っていただき、ありがとうございました。
Thank you for helping me.
資料を確認していただきたいのですが、よろしいでしょうか。
I'd like you to check the materials — would that be alright?