Short for "malicious software," malware refers to software programs designed to damage or do other unwanted actions on a computer system. In Spanish, "mal" is a prefix that means "bad," making the term "badware," which is a good way to remember it (even if you're not Spanish).
Common examples of malware include viruses, worms, trojan horses, and spyware. Viruses, for example, can cause havoc on a computer's hard drive by deleting files or directory information. Spyware can gather data from a user's system without the user knowing it. This can include anything from the Web pages a user visits to personal information, such as credit card numbers.
It is unfortunate that there are software programmers out there with malicious intent, but it is good to be aware of the fact. You can install anti-virus and anti-spyware utilities on your computer that will seek and destroy the malicious programs they find on your computer. So join the fight against badware and install some protective utilities on your hard drive!