Hostages are at the heart of the fragile cease-fire between Israel and Hamas, now in its fifth day. As of Monday night, 50 Israeli hostages had been released, as had 150 Palestinian prisoners. More releases were expected on Tuesday, under what Qatari mediators said was a deal to extend the cease-fire by two days. Isabel Kershner, a Jerusalem-based reporter for The New York Times, explains how a grass-roots movement managed to pause the war, and what it will mean for the rest of the conflict.