P. Xavier is the brain dead twin of Charles Xavier.
It is unknown what happened to him between his birth and X-Men: The Last Stand, but it is known that at some point, he was placed under the care of Charles' old friend Moira MacTaggert on Muir Island.
Charles gave a lecture about his brother, asking if it would be possible to transfer the consciousness of a dying father of four children with terminal cancer into the body of the brain-dead patient. Later, after his body was destroyed by Jean Grey, who was possessed by her Phoenix alter-ego, Xavier transferred his mind to the body of his brain dead twin in order to escape death.
When Logan returns to America, Charles approaches him in his brother's body, though he still somehow still needed a wheelchair to move around since his brother's body is alluded to be in a restricted movement due to being in a coma for a long time and brain-dead since birth.
Charles would continue to use his brother's body for the next eight years, up until the last surviving members of the X-Men send Wolverine back in time to 1973 in order to prevent the creation of the Sentinels. After an unknown period of time, the Sentinels found the remaining X-Men and were about to fire on them, including Charles (in P. Xavier's body), before Shadowcat lets go of the time-traveling Wolverine, erasing their timeline and changing their past and future.
Given that Logan (possessing his past self with help from Kitty's power of chronoskimming), guided Charles to prevent the dystopian Sentinel-ruled future by using his knowledge of future events such as Jean Grey's death to change the past, it's possible that in the revised timeline, Charles taught Jean to control her powers rather than repress them, which could possibly have prevented his death at her hands in 2006. If that is the case, Charles would have no need to possess P. Xavier's body.Charles is seen alive and well as of 2023, therefore, his brother is presumably still in a brain dead, comatose state.