Mastitis is the word used to describe an infected blocked milk duct. It is a condition that is quite uncomfortable for the nursing mother, but it does not need to signal the end of breastfeeding. You will likely have a hot red area on your breast at the site of the infection and have a fever.
If you do have mastitis, it is important to continue emptying the infected breast (and not neglecting the other side) by increasing the frequency of breastfeeding on that side or by pumping. Mastitis will not harm the baby, and the baby can be very helpful in relieving any fullness the mom may be experiencing. It is also important to call your doctor or healthcare provider as the standard method of treatment is to put the mother on antibiotics.