If passwords provide a 'door' to cover the 'doorway' into your 'house', then firewalls provide 'shutters' to cover the 'windows'. Bear with me, we're extending the metaphor further than we probably should.
Your network has a lot of windows. These aren't just casual windows that let you see out, the metaphor is closer if you think of them as service windows, like at a drive-through of them have people (programs) at them to provide service, some of them are empty.
A firewall provides shutters to close the empty service windows.
A firewall does absolutely nothing to protect the windows you leave open - that's the job of the programs which provide the services at those windows. But if you don't have a firewall, there's all those empty windows that an intruder can use to break in through.
The firewall is ideally a separate computer which is between your network and the internet. It can be a purpose-built device - there are some available which are small black boxes which look like network hubs. Or it can be your brother's old 486, with a highly secure operating system that provides an inbuilt firewall. Whatever you choose, ensure that your local computer expert approves of it, and do your best to ensure that he knows how to make sure it really is secure.
None of your computers should be able to access the internet or be accessed from the internet without going through the firewall.
The technical term for the windows is 'ports'.