Melisandre and Stannis Baratheon have sex, with Melisandre promising to give Stannis 'a son'. After the failed parley between Stannis and Renly, Melisandre is revealed to be pregnant. She gives 'birth' to a shadow in a cave close to Renly's encampment. Ser Davos Seaworth watches in horror. The creature later sneaks in to Renly's camp and assassinates him before vanishing.
In the books
In the Song of Ice and Fire novels, Melisandre actually conjures forth two shadows on separate occasions to deal with Stannis's foes. She needs to use Stannis's own life-essence to fuel the entities, but this hugely drains him. Use of the creatures is thus limited in case their creation taxes the creator to the point of death.
Fans colloquially call the creatures 'shadow babies' due to the nature of their creation.
- Shadows at A Wiki of Ice and Fire (MAJOR spoilers from the books).