Claudia gives birth to Jacob & the Man In Black, Mother kills her with a rock

At the caves, Mother sits with a mortar and pestle, grounding up something to help Claudia's wounds. Claudia is eating some food and asks where the rest of Mother's people are, and Mother says that it is just her. Claudia asks how she got to the island and other says the same way she did, by accident. Claudia starts to ask "How long have you..." and Mother interrupts her and says "Every question I answer will simply lead to another question."

Claudia says there were other people on her ship and Mother suddenly interrupts her and says if there are other people on the island, she will find them. Claudia then starts to wince in pain as the baby starts coming.

Some time passes and Mother is helping Claudia give birth to her baby. After struggling, the baby is born and Claudia says that his name is Jacob. Mother sits him on a blanket and looks at him happily. Then, Claudia starts struggling again and Mother looks concerned. She discovers that there is another baby that she is giving birth to. After the other baby is born, Claudia says she only picked one name, so the Man In Black still has no name.

Both babies are laying next to each other, Jacob wrapped in a white blanket and the Man In Black in a black blanket. Also, Jacob is calm and looking around, while the Man In Black in crying.

Claudia asks to see the babies, then Mother moves over her and says "I'm sorry." She then bludgeons Claudia to death with a rock. We hear the repeated blows as we look at the two babies.

So it seems that Fake Locke wasn't completely lying about when he told Kate that he had a crazy mother, and we see more of that later in the episode.

Emily Locke in Hosptial gives birth to John

Here we see Emily at the hospital after she is hit by the car. She tells the nurse that she is almost six months pregnant. She then gives birth to John Locke and he is put into isolation due to being premature. She yells to the nurse to name him John.