Mahmoud Abbas heads the PLO Executive Committee. the Executive Committee hand-picks the members of the PLO National Council.. The Council then chooses members of the Executive Committee. The EC then elects the chairman of the committee - Abbas.
The PLO Executive Committee is the government of the "State of Palestine" recognized by the UN.
The Palestinian Authority is politically meaningless, even though Abbas heads that as well. Of course, he was "elected" to that symbolic position back in 2005, and there have been no elections since.
Mahmoud Abbas isn't the "president." He's the dictator.