To put it simply, a computer virus is just a small computer program that can replicate itself and place itself on a computer without the computer user knowing it. They typically come attached to other files. These files are typically executable files with a (.exe) file extension. People often use the term virus to mistakenly label other troublesome programs that are really malware or adware. There is a difference. Most malware and adware do not replicate themselves and therefore are not technically considered viruses. However, these days, malware is a far more common type of infection. Other things that can infect a computer but aren't really viruses are things like computer worms and Trojan horses.
Trojan horses are very common these days. As their name implies, they often sneak into a person's computer because they come packaged as a useful program like a screensaver or something. Then, once they are installed on the computer, they open up ports (like a secret door to the internet) on your computer and allow other types of infections to sneak in. These other infections come in totally unannounced. You won't realize they are there until your antivirus program happens to detect them. By then, it is possible that their intended damage has already occurred.
This is why it is important to have a firewall on your computer. The firewall increases the computer's security by closing all of these doors and locking them. The firewall only allows doors to open that are used by common programs like web browsers and email. For another port (door) to be opened, the firewall program usually asks for permission from the computer user. That's why you get the messages popping up in the lower right hand corner of your computer asking if it is okay for something to happen.
Another type of infection is the computer worm. Computer worms are like viruses except they do not come attached to any other files. These worms can move from computer to computer across a network. They move from computer to computer by going through open ports. This is the biggest benefit of having a firewall to keep those ports closed and locked. The internet is one giant network. So, just by being connected to the internet, your computer is exposed to this type of infection.
Adware is another type of program all together. Typically, these program come bundled with other software as well. When downloading some music sharing software, if you read all the fine print you would see that the reason that software is free is because it comes bundled with an adware program. The adware program will make pop ups come up on your computer. It might also modify your internet browser so that your search results are influenced in some way that benefits the author of the program.
I can honestly say from experience that you can guarantee getting an infection by using your Windows based computer to browse the internet regularly if you do not have an adequate firewall on your computer. The firewall is far more important than your antivirus software itself. This is one of the most misunderstood computer security issues among the general public.

The Creeper virus was first detected on ARPANET, the forerunner of the Internet in the early 1970s.^[3] Creeper was an experimental self-replicating program written by Bob Thomas at BBN in 1971.^[4] Creeper used the ARPANET to infect DEC PDP-10 computers running the TENEX operating system. Creeper gained access via the ARPANET and copied itself to the remote system where the message, "I'm the creeper, catch me if you can!" was displayed. The Reaper program was created to delete Creeper.^[5]

A program called "Rother J" was the first computer virus to appear "in the wild" — that is, outside the single computer or lab where it was created.^{[citation needed]} Written in 1981 by Richard Skrenta, it attached itself to the Apple DOS 3.3 operating system and spread via floppy disk.^[6] This virus was created as a practical joke when Richard Skrenta was still in high school. It was injected in a game on a floppy disk. On its 50th use the Elk Cloner virus would be activated, infecting the computer and displaying a short poem beginning "Elk Cloner: The program with a personality."

The first PC virus in the wild was a boot sector virus dubbed (c)Brain^[7], created in 1986 by the Farooq Alvi Brothers, operating out of Lahore, Pakistan. The brothers reportedly created the virus to deter pirated copies of software they had written^{[citation needed]}. However, analysts have claimed that the Ashar virus, a variant of Brain, possibly predated it based on code within the virus.^{[original research?]}

Before computer networks became widespread, most viruses spread on removable media, particularly floppy disks. In the early days of the personal computer, many users regularly exchanged information and programs on floppies. Some viruses spread by infecting programs stored on these disks, while others installed themselves into the disk boot sector, ensuring that they would be run when the user booted the computer from the disk, usually inadvertently. PCs of the era would attempt to boot first from a floppy if one had been left in the drive. Until floppy disks fell out of use, this was the most successful infection strategy and boot sector viruses were the most common in the wild for many years.^[8]

Traditional computer viruses emerged in the 1980s, driven by the spread of personal computers and the resultant increase in BBS, modem use, and software sharing. Bulletin board driven software sharing contributed directly to the spread of Trojan horse programs, and viruses were written to infect popularly traded software. Shareware and bootleg software were equally common vectors for viruses on BBS's.^{[citation needed]} Within the "pirate scene" of hobbyists trading illicit copies of retail software, traders in a hurry to obtain the latest applications were easy targets for viruses.^{[original research?]}

Since the mid-1990s, macro viruses have become common. Most of these viruses are written in the scripting languages for Microsoft programs such as Word and Excel and spread throughout Microsoft Office by infecting documents and spreadsheets. Since Word and Excel were also available for Mac OS, most could also spread onto Macintosh computers as well. Although the majority of these viruses did not have the ability to send infected e-mail, those viruses which did took advantage of the Microsoft Outlook COM interface.^{[citation needed]}

Some old versions of Microsoft Word allow macros to replicate themselves with additional blank lines. If two macro viruses simultaneously infect a document, the combination of the two, if also self-replicating, can appear as a "mating" of the two and would likely be detected as a virus unique from the "parents."^[9]

A virus may also send a web address link as an instant message to all the contacts on an infected machine. If the recipient, thinking the link is from a friend (a trusted source) follows the link to the website, the virus hosted at the site may be able to infect this new computer and continue propagating.

Cross-site scripting viruses emerged recently, and were academically demonstrated in 2005.^[10] Since 2005 there have been multiple instances of the cross-site scripting viruses in the wild, exploiting websites such as MySpace and Yahoo.