The phrase "warms the cockles of my heart" is an idiom used to express a feeling of deep-seated contentment or satisfaction, a heartfelt sort of warmth. It typically signifies a strong positive reaction towards something that makes one feel happy or affectionate.

The phrase has an interesting origin that is rooted in both human anatomy and Latin language. The term "cockles" comes from the Latin term "cochleae cordis", meaning 'the ventricles of the heart'. In ancient medical texts, "cochleae" was used to describe the chambers of the heart because of their resemblance to the shape of a cockleshell (the shell of a small, edible mollusk).

In the 15th century, the Latin term was adopted into English as "cockles", and over time it became associated with the idea of warmth and affection because of the heart's symbolic link with love and emotion. So, when someone says something "warms the cockles of their heart", it's a rather poetic way of saying that it makes them feel good deep down in their very core.

Despite the anatomical origins, the phrase is more poetic and colloquial than medical, and it's a charming way to express strong feelings of happiness, satisfaction, or gratitude. It's often used in reaction to a good deed, an act of kindness, a touching story, or anything else that evokes a strong, positive emotional response.