One-way firewall
A one-way firewall only protects you against external threats. This is done by the firewal blocking anything, that is not permitted. This means, that you can not get infected by malware, unless you allow it yourself. You can easily destroy programs or files accidentally, when downloading something from the internet, you are unsure of. In the case of an infection, it is important to have an antivirus program, that can discover and remove the malicious programs and files.
Hackers constantly develop new techniques
Hackers have tailored their techniques to cause harm to your PC. The new malicious programs are created so that their harmful programs stay on your computer. Earlier, malware was built to gain access to your PC, cause a harmful action, and then destroy itself along with the contents of your PC. Newer malware is built to stay on your PC for as long as possible. This means, that your computer might already be infected, and that your sensitive information can be collected, when you send emails, log in to netbank, etc.
Dual firewall
A dual firewall protects you from both external malware and malware, that is already on your computer. If you already have malware on your computer, you will be an easy target for additional attacks over a longer period. Therefore, it is not sufficient to protect yourself with just any antivirus program. If you have an antivirus program, that is unable to discover and delete the infection, it is important to shut off the internal cummunication using a dual firewall.