When something is unifying, it causes people to unite. You and your brothers and sisters might not have much in common, but find that watching TV together is a unifying force in your lives: it brings you all together.
If a country unites in grief over a lost leader, that leader's death could be said to have a unifying effect on the nation. During the East Coast blackout of August 2003, the lack of electricity turned out to be unifying for New Yorkers, who gathered to drink quickly warming beer and soon-to-melt ice cream.
