This is the 8452nd most frequent Japanese word.
懐
"懐" (ふところ) refers to the bosom, heart, or one's emotional/physical inner space; it can also mean pocket or money on hand.
In this sentence, '懐' refers metaphorically to the emotional heart or inner feelings, portraying warmth and kindness.
彼女の話を聞いて懐が温かくなる気がしました。
Listening to her story, I felt warmth in my heart.
Here, '懐' is used literally to indicate a pocket or a part of clothing where items can be carried close to the body.
財布を懐に入れておきなさい。
Keep your wallet in your pocket.
In this case, '懐' serves as a root within '懐かしい' (nostalgic), implying an emotional connection to cherished memories.