When you use internet, you are connected to millions of PC’s out there. And each PC have its own unique address known as Static IP Address. This gives your identification by locality.
Without a firewall, on a typical computer, even if well maintained, a remote person will still be able to know that the communication effort has reached some computer, and perhaps some information about the operating system on that computer. If that computer is handled well, the remote user will not be able to get much more information from your computer, but might still be able to identify also who your ISP is, and might decide to invest further time in cracking into your computer.
With a firewall, you can set the firewall so that any communication effort from remote users (in the better firewalls you may define an exception list) will not be responded at all. This way the remote user will not be able to even know that it reached a live computer. This might discourage the remote attacker from investing further time in effort to crack into your computer.
Again there is one more security confirmation you can do is running is operating behind proxies. It is the safest method but sometimes all web pages can not be surfed So selecting a firewall can be a good idea.