The "ice" is the figurative coldness when strangers are gathered together for the first time. No-one is actually unfriendly, but no-one really knows what to say or do either. The mood is still, silent and unmoving, like a frozen lake. You can even say the mood is simply "icy". It follows that the act of breaking this "ice" means to do something to help the people relax and begin talking. Something like a game, a conversation-starter or some entertainment.

To get beyond the first uncomfortable/embarrassing feelings when meeting people for the first time, by way of conversation or action.

yup " breaking the ice" means -- making things clear...pulling the carton of hesitation..... for example --- father and his son breaking the ice after so long...meaning ---from long time here was cold relation between both father and son whatever due to miss understand or something els.. but now they both are avoiding this by a warm conversation and by making things clear by self expressing eachother..