A brown-out is a condition of lower than normal power line voltage being supplied by your local utility or generating equipment. This condition may be short term (minutes to hours) or long term (1/2 day or more). A power line voltage reduction of 8 - 12% is usually considered a brown-out.
A black-out is a complete loss of power for whatever reason and is usually short term, as it is so serious that the generating company will classify the situation as an emergency. However, just occasionally a catastrophe may cause a longer term black-out.