What is malware?
Malware, short for malicious software, is a blanket term for viruses, worms, trojans and other harmful computer programs hackers use to wreak destruction and gain access to sensitive information. In other words, software is identified as malware based on its intended malicious use, rather than a particular technique or technology used to build it.
This means that the question of, say, what the difference is between malware and a virus misses the point a bit: a virus is a type of malware, so all viruses are malware (but not every piece of malware is a virus).
History of malware
Malware has a long, storied history, dating back to infected floppy disks swapped by Apple II hobbyists in the 1980s and the Morris Worm spreading across Unix machines in 1988.