In the books
In the A Song of Ice and Fire novels, the Gulf of Grief is a busy sea, with ships from the Free Cities and the Jade Sea crossing it to reach the city-states of Slaver's Bay. It is not uncommon for ships to become becalmed whilst crossing it. Ship captains prefer to sail across the center of the gulf and along the eastern coast, as it is held to be bad luck to sail within sight of Valyria.
During the Doom of Valyria, substantial tidal waves and tsunamis generated by the collapse of the landmass into the sea raced across the gulf, laying waste to many cities and kingdoms along its shores and on the islands. This may be the reason for the term 'grief' in the title.