Over the years Mahmoud Abbas has stated that he is quitting numerous times. Meanwhile his on again-off again talks with Hamas seem to be on again. If these reports are true, he intends to stay in power as Prime Minister of the Palestinian Authority in a unity government with Hamas (possibly in addition to remaining President).

Ma'an adds some possibilities:

Sources close to Abbas, who wished to remain anonymous, told Ma'an that the decision is not certain and that the role of prime minister could be an added burden on the President.
Other sources from the meeting said that Hamas chief Khalid Mashaal had suggested Abbas for the role of prime minister.

The New York Times reports:

The Palestinian Information Center, a news Web site closely affiliated with Hamas, reported that the two sides had reached “a preliminary agreement that Abbas take responsibility for the government in the coming phase.” Maan, an independent Palestinian news agency, also reported a proposal that would have Mr. Abbas serve as prime minister.
The information, however, could not be immediately verified. The Palestinian news sites cited anonymous sources. Hamas officials contacted in Gaza on Sunday night did not confirm the reports.

Previous announcements of agreements seem to have vanished in the haze. Regardless of the outcome, Abbas freely negotiates with a terrorist organization without preconditions and is widely considered a moderate; he refuses to negotiate with Israel without preconditions and Prime Minister Netanyahu is roundly condemned for not doing more to get Abbas back to negotiations.