Bags under the eyes come naturally with age. Eye bags are such a common problem because the skin under the eyes is among the thinnest and most sensitive layer. Bags can be due discoloration of the skin or swelling. Discoloration of the skin are due to pigment changes and can be due to dilated blood vessels which can be caused by allergies, extreme hot/cold changes and rubbing your eyes. Discoloration is usually due to sun exposure and smoking.
What can you do to prevent or hide them? Use concealer or foundation. Try using eye products with Vitamins B, C, E or soy to help reduce signs of sun damage and help reverse signs of aging. Eye creams with retinol also help minimize sun damage (pigmentation). Cold compresses can help reduce the swelling and caffeinated tea bags constricts blood flow to the area cutting down on swelling.
If the above interventions do not solve your problem, best to see a Dermatologist who can recommend something more invasive such as lasers and fillers.