The way I understand it, is that the Router translates the internal IP address to a another address (spoof) and this is what is presented to the Internet Your real IP address is not open for inspection!!
Some routers have many firewall-features, others have not. Every brand and every type has different features and options, so check specifications about a router before you buy it.
Btw. maybe means "natural firewall" that the cable-modem isn't directly attached to your computer, so an atacker doesn't have direct access to your machine when you don't setup portmappings.