In the books
In the A Song of Ice and Fire novels the Second Sons are one of a number of mecenary companies operating in Essos. They are so-called because it is common for the second sons of lords and merchants - who would otherwise inherit nothing - to seek service in their ranks for glory and gold. Aegor Rivers, known as Bittersteel, served in the Second Sons for a year before leaving to found the Golden Company. Prince Aerion Targaryen also joined the Second Sons during his time in Essos.
Prior to the novels, the Second Sons had recently fallen into disrepute due to the rise of a particularly vicious commander, a braavosi called Mero. Mero has led the company in pursuing contracts no-one else would touch, and the company has become almost as ill-omened as the infamous Brave Companions as a result. Mero's reputation grew so bad that none of the Free Cities would hire the Second Sons anymore, which is why at the time the books commence the Second Sons are in the employ of the city of Yunkai in Slaver's Bay.
The series combines the Second Sons with the Stormcrows, company led by Prendahl na Ghezen, Sallor the Bald, and Daario Naharis.