To unfurl something is to roll it out, unwinding it the way you do with a coiled laptop charger cord. You might also unfurl a pair of socks curled around each other or the American flag you keep rolled up in a closet until the Fourth of July. Unfurl is a more common word than its opposite, furl, which means "roll or fold." The French origin is ferler, "to furl," from the Old French roots fer, "firm" and lier, "bind."