Antivirus
Originally antivirus software protected your computer from viruses, however now antivirus software fights against a host of threats including viruses, worms, trojan horses, phishing attacks and other malware.
Firewall
A firewall, simply put, is a protective barrier between the internet and your computer to keep harmful, destructive forces from entering. It can either be a hardware device or a software program that acts like a protective barrier between your computer and the internet.  This firewall protection filters all the packets of information (small chunks of data) coming into your computer via your internet connection and anything flagged by these filters is denied entrance into your computer.
Anti-spyware
Anti-Spyware is a software program that scans and removes from your computer’s hard drive all known spyware that has been installed in a stealthy way and without your consent. It is also designed to prevent these unwanted spyware installations which are geared towards collecting private information about you, interfering with your control of your computer, e.g. redirecting your web browsing and forcing your computer to access unwanted websites, changing your web home page, changing your computer settings. The common ways to get spyware are by downloading free software over the internet or by visiting non-reputable websites. Not all free software contains spyware and most actually disclose any additional software added on that may be spyware within their license agreement.  Always read carefully before you install things on your computer.
Anti-malware
Anti-malware is a blanket term used to cover antivirus programs, intrusion detection systems as well as spyware blockers and other software that not only detects but eliminates unwanted programs that have come into your computer via the internet.
Internet Security
Internet security is a program designed to prevent unauthorized access as well as damage to your computer through the internet by using a combination of protection against viruses, spyware, spam and identity theft.  It includes a firewall and many now also include parental controls to limit/block Web sites with inappropriate content for children using the home computer.