expression, i-adjective
broad-minded; generous; tolerant
Describes a person who is open-hearted, accepting, and not petty. Often used to praise someone's character. The expression is a set phrase; the adjective 深い modifies 懐 (ふところ, 'bosom' or 'heart').
See also: 懐が深い
彼は懐の深い人で、誰とでも仲良くなれる。
He is a broad-minded person who can get along with anyone.
あの先生は懐の深いから、どんな質問でも真剣に聞いてくれる。
That teacher is so tolerant that he listens seriously to any question.