The Palestinian Liberation Organization (PLO) is the national representative of the Palestinian people. It runs the Palestinian National Authority (PA), the semi-autonomous government tasked with managing the Palestinian territories until it makes a deal with Israel. Fatah, the secular nationalist political party that’s dominated Palestinian politics for decades, controls the PLO and PA.
In practice, the PLO runs the government in the West Bank but not in Gaza, which is governed by Hamas. It also conducts peace talks on behalf of the Palestinians, but its authority to implement those deals has in the past been hampered by poor relations with Hamas.
In the first decades after its 1964 creation, the PLO sought to destroy Israel and replace it with an entirely Palestinian state. Fatah’s founder, Yasser Arafat, employed military tactics toward this end, including attacks on Israeli civilians. This changed in 1993, when the PLO accepted Israel’s right to exist in exchange for Israel recognizing it as the legitimate representative of Palestinians. That was the beginning of real peace negotiations between the two sides.
The PLO’s current chair is the relatively moderate Mahmoud Abbas, whose opposition to violence played a role in de-escalating the second intifada. Frustrated by the failure of peace talks, particularly Secretary of State John Kerry’s push in 2013 and early 2014, Abbas is also pursuing international recognition of Palestinian statehood. As a result, Palestine now has non-member state status at the UN; it also joined the International Criminal Court on April 1, 2015.
The statehood push is meant to put pressure on Israel. The US opposes it.