reincarnation effect causes the sum total of her life's experience to travel back in time at the moment of her death, imbuing her with a lifetime's knowledge from the womb; secondary effect makes her opaque to detection as a mutant by telepaths, precogs, technology, etc.
Moira MacTaggert was a geneticist and one of the X-Men's long running human allies for years. She was allegedly the first human to contract the Legacy Virus in Excalibur (1st series) #80, and died in a conflict with Mystique in X-Men (2nd series) #108.
In House of X #2, however, it was revealed that Moira X was a mutant with the power of reincarnation, on her 10th life. It was also confirmed she was still alive, having faked her death using a Shi'ar golem.
Allegedly, Moira's reincarnation annihilates and reboots the timeline each time she dies, a curious interpretion of multiversal theory for the Marvel Universe which hasn't been strictly tested. In Inferno (2nd series) #4, a version of Forge's Neutralizer tech cancelled her powers, presumably meaning she can now die without impacting the timeline.