The physical experience of any emotion is due to chemicals released in the brain. The heart, the largest of our involuntary muscles and most constant in its activity, responds to this chemical release in very noticeable ways (beats faster, harder, slower, softer). We 'feel' these changes and, logically, associate them to how we 'feel'. Akin to this is 'butterflies in the stomach'. Some cultures even believed emotions derived from the gut.