A firewall will prevent access to your computer by hackers, who are otherwise able to look through your files, steal confidential information, infect your computer with malicious code like Trojan horse programs and use your computer for storing and distributing nasty stuff like spam and pornography. (A computer taken over by hackers can become a Zombie computer and be used to send out thousands of spam emails or to store pornographic images for others to download.)
(The complete Windows Trojans paper Frame4 Security)
Not having a firewall is like leaving your front door unlocked. However, it's easy to see when you have been burgled, but not when you have been hacked. The theft of confidential information might not be noticed for weeks, and your computer could be working for a hacker without your knowledge.
How to detect a hacker attack viruslist.com
You can test the security of your computer, and find out if your front door is open at one of these sites:
(I have seen criticism of the first two sites for being biased and misleading respectively. However, if either reports that your port are open, I think it's fair to say that you should be worried. With any good firewall installed properly, ports should be closed.)
To securely lock your front door, you need to block the ports of your computer (the doorways through which information passes.) A firewall will do this and block any attempts by hackers to gain access to your computer by means of an external connection.
Some firewalls can also block programs on your computer from connecting to the internet, and thereby deny any attempt by a Trojan horse programs which does get onto your computer to use the internet: Trojans are harmless if they can't relay information to their creator. The problem here is that many legitimate programs need to contact the internet, so the firewall program must help the user to identify legitimate programs and allow them access to the internet- this usually involves a 'learning period' after installation during which the user is prompted by a pop-up dialogue box to allow or deny internet access.)
For more information:
Why do I need a firewall? zonelabs.com
Home PC firewall guide firewallguide.com
Firewalls Wilders Security Advisors
The next page gives information about free firewalls.
Before installing, scan your computer for any Trojans already present.
Run a scan using your anti-virus program - update the definitions first - (See anti-virus page.)
NB A computer connected to the internet for any period (especially via broadband) without protection from a firewall may have been compromised: a hacker may have gained control of the computer. In these circumstances, reformatting of the hard drive and reinstallation of the operating system may be necessary to guarantee that control of that computer is returned to the user. This may be advisable for users with confidential information on their computers, or for anybody who uses a credit card for internet shopping.
The Antivirus Defense-in-depth Guide microsoft.com