From A Wiki of Ice and Fire
A shadow assassin is a form of magic used by Melisandre to murder Lord Renly Baratheon and Ser Cortnay Penrose during the Siege of Storm's End. Since a shadow is a "servant of the light", the sorceress is able to invoke the human-like shadow assassin and direct it against her enemy. The shadow assassin is implicitly formed through an act of sexual intercourse between Melisandre and her liege, King Stannis Baratheon so they are also known as Shadow Babies. After a period of "gestation", Melisandre can invoke the shadow assassin by "birthing" it. During the birth, the shadow assassin is visible and takes the form recognizable as Stannis Baratheon. Later, the shadow assassin becomes more shadow-like and difficult to detect by eye. The shadow assassin is armed with a sword, similar to the flaming sword wielded by Stannis. When the shadow assassin attacks its target it is nearly invisible. It uses its sword and stabs for the neck before disappearing.
The effect on Stannis Baratheon is significant. He appears to have aged years after siring a shadow assassin on Melisandre. Perhaps this is why no shadow assassin is used during the Battle of the Blackwater. Stannis perceives the actions of the shadow assassins as their own through dreams.