'Break the ice' usually means "do or say something to relieve tension". For instance, both of your friends, who are currently fighting, meet up with you. The atmosphere would surely be awkward and you're friends will certainly be quite, refusing to speak to each other. Now, you need to 'break the ice' - that means you need to do something to break that kind of atmosphere.
Break the ice could also mean to "get conversation going going at the start of the party or when people meet for the first time". It quite connected to the first definition actually.