generous; big-hearted; magnanimous
Describes a person who is broad-minded, tolerant, and not bothered by small things. Often used to praise someone's character.
He is a big-hearted person and is kind to everyone.
気の大きい態度で、失敗を許してくれた。
With a generous attitude, he forgave my mistake.
A set phrase combining 気 (spirit, mind) and 大きい (big), literally 'big-spirited'. The exact origin is uncertain, but it follows a common pattern of describing personality traits with 気.