How are breasts suppose to feel?

Each breast has milk producing glands (also called lobules or alveoli) that make milk from the nutrients and water they take from the bloodstream.

Secondly, there are milk ducts that carry the milk to the nipple from the milk glands. The system of milk glands and ducts resembles several bunches of grapes: the glands are the grapes, the ducts are the stems. Like grapes come in bunches, the milk glands and ducts also are organized into several clusters that are called lobes. The breast actually has 15-20 of these lobes or grape bunches in it. From outside, the lobes feel like little nodes or lumps especially before menstruation.

The female breast.

The space in between the lobes is filled with connective and fatty tissue. Fat also surrounds the whole system of milk ducts and glands. Usually the breasts of young women are mainly glandular tissue and that is why their breasts are firmer. The softer the breasts are, the more fat they contain.

Note that the breast does not have any muscles (except for tiny ones in the nipples), so no amount of exercise will change their appearance. The breast is supported by semi-elastic bands of tissue called Cooper's ligaments. These ligaments (along with the skin) stretch over time when the gravity pulls the breast down, and that is why the breast will start drooping or sagging.

The breast size and shape in different women varies a lot. Some women have more glandular tissue in their breasts, some have less. Some have more fatty tissue than others. Some have more connective tissue so their breasts are firmer, and yet some women are totally flat-chested. The size and shape also varies over time in the same woman because of the changes during menstrual cycle, pregnancy, after weaning, and during menopause

Yes that's all fatty tissue and muscle in that lump. We all have that. And it's very common for breasts to get sore or ache at certain times of the month. Just another joy of being a woman :-)