Cards of the same color are called suited. With suited starting hands, the hope is for a flush (5 cards of the same color). The chances are, however, not very good. The probability is just 5.77%.
A somewhat better chance if the cards are connected (suited connectors). When playing these starting hole cards, there is still a chance for a Straight, Straight Flush, or with cards such as AKs even a Royal Flush.