Basic definitions

(These are definitions in my words. For more accurate definitions, refer wikipedia.)

Computer virus: It's a software program, not desired to be running in your system. (Contrary to this definition, microsoft products are not counted as Viruses ;) :P).

Computer viruses show similar symptoms as living-viruses (or for that matter, humans too).
1. They hog your system resources.
2. They spread to other systems & infect them also.
3. They can corrupt the data on your system for their purpose - spreading.

There are multiple types of these unwanted programs like
- Virus,
- Spywares (these can upload your personal data on web without your knowledge),
- keylogger (mainly for stealing passwords),
- trojens (they try to steal your information & can allow external user to control your computer),
- etc.
For more correct definitions of these, please refer google / wikipedia.

Antivirus: It's the program that does/tries/claims to remove virus threats from your system. They have definitions of known viruses as their database. These definitions are nothing but some patterns that are commonly seen in these virus files.
Similar to antivirus, there are anti-spywares, which are designed to remove spywares from computer systems.

Firewall: Apart from the virus infection on files on your system, there is another source of threat - the network. Network threats include many types of attacks like IP address forging, DNS response forging, denial of services attack etc. These network related attack are taken care of by the firewall. firewall protects your computer against these network attacks. There are many more related terms, but those may not be required at this stage & will be covered in the individual post, if required.