Broadcasts are stopped at a layer-3 boundary (router). An example of a broadcast is an ARP request where a host is looking for the MAC address of the owner of an IP address. The host sends a broadcast asking, "Who owns this IP address?" Broadcasts are received and processed by every host in the layer-2 domain.
A multicast is received and processed by hosts which subscribe to the multicast group of the multicast. It is an elective "broadcast". Many things use multicast, including some routing protocols. An example of multicasting is an IPTV application which some companies use. Multicasts are normally stopped at a layer-3 boundary (router) unless the router is configured for multicast routing, which is a large topic which cannot be adequately addressed here.
Since broadcasts are stopped at a layer-3 boundary, and multicasts only traverse layer-3 when all the routers in the path are configured to do multicast routing, broadcasts and multicasts cannot traverse the Internet, which is why all your internet traffic will be unicasts.
By the way, IPv6 has eliminated broadcasts; there is no such concept in IPv6. IPv6 makes heavy use of multicasts. You may also see the term anycast used a lot in IPv6, but IPv4 can use anycasting, too. Anycasts are really unicasts, so the unicast rules and concepts apply to anycasts.