Kovarian

The Eye Patch Lady was a mysterious woman of whom Amy Pond had recurring visions. She wore an eyepatch or a similar device over her right eye.

The first time Amy saw her was when she appeared at the little girl's bedroom door at Graystark Hall Orphanage. She appeared through a hatch in the door, which later disappeared. Amy was startled by the woman and asked who she was, but the woman ignored her and said "No, I think she's just dreaming". When Amy entered, the room appeared to be empty, with no evidence of the woman or the hatch. (DW: Day of the Moon)

While asleep on a pirate ship, Amy was woken by a noise and saw the woman in a hatch that opened on the hull of the ship. The woman said, "It's fine. You're doing fine. Just stay calm", and then she vanished instantly, along with the hatch. (DW: The Curse of the Black Spot)

Amy twice saw the woman again at an acid mining factory, the first whilst she was searching for Rory Williams, though she did not speak. The next time Amy saw her, she was able to sense the woman's appearance, staring at the point on the wall where the hatch would open, beforehand. When mentioning this woman to the Doctor he quickly attempted to reassure her by dismissing it as "time memory, like a mirage." (DW: The Rebel Flesh/The Almost People)

After her ganger form was destroyed, Amy awoke to find herself in a hospital with the lady acting as her midwife. She then went into labour with the lady instructing her to push. (DW: The Almost People)

Behind the scenes
The "Eye Patch Lady" appeared under various circumstances to Amy Pond, always through a gap in a surface that subsequently disappeared. Up until the spring finale of Series 6, the lady's identity was not revealed and so her various appearances (shown below) acted as a story arc.