In regular, healthy women and men, small bumps may appear on the surface of the skin around the nipple area (areola) and the nipple itself. These are called Tubercles of Montgomery or Montgomery’s glands. They are absolutely normal, and you have nothing to worry about.
Montgomery’s glands are sebaceous glands that secrete oily fluids to keep the areola and nipple moistened and protected from germs. If you are breastfeeding, these glands also function as an olfactory stimulus to the nursing baby.

Young women in their 20s may observe that these bumps become more prominent. This is due to natural growth and development of their bodies. Changes in hormones, especially around menstrual cycle, pregnancy, or much earlier during puberty, often cause these tubercles to enlarge. 

However, if you feel these bumps are painful, itchy or red, consult a gynaecologist or a dermatologist. These glands can become blocked or inflamed causing irritation. The changes could be due to an ill-fitting bra, or a skin condition like eczema or folliculitis or, in rare cases, cancer.

If you feel the problem is persistent, painful or that the bumps increasing in number see a doctor right away.

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The information provided in Dr. Dixit's answer is for educational purposes only and is not intended to constitute medical advice. The information provided should not be relied upon as a substitute for consultations with a qualified health professional who may be familiar with your individual medical needs.