Widow's Wail is a Valyrian steel sword made out of an old Stark heirloom, the greatsword Ice. Tywin Lannister commissioned Tobho Mott, a master armourer of King's Landing, to reforge Ice into a new sword and he sucessfully managed to reforge it into two new swords.
Widow's Wail was a wedding present from Tywin Lannister to his grandson, King Joffrey. The sword was later passed to Joffrey's brother, King Tommen. Its sister-sword, Oathkeeper, was given to Brienne of Tarth by Jaime Lannister to aid her in her pursuit of Sansa Stark, and as a symbol of his new sense of morality (hence the name).