The YAHOO email account of my younger daughter was just “hacked” and spam messages were sent to her address list using her account. You can usually avoid this kind of attack by following these three rules:
1. Use strong passwords (at least 8 digits using upper & lower case plus numbers & special characters)
2. Don’t use the same password for all your accounts.
3. Regularly scan your hard drive for Malware with updated anti-malware software.

Here are the definitions you asked for:

Malware is malicious, basically anything bad that you don’t want. ( In law, malware is sometimes known as a computer contaminant)

A computer virus is malware that can reproduce itself, the term is sometimes used erroneously to refer to the entire category Viruses require human interaction. In the early days, this was often giving a floppy disk to a friend who then put it in his computer. These days it means double-clicking an email attachment or visiting a website.
Spyware is like a spy, it secretly steals information.  It is used to monitor/Log the activity performed on a computer. These are used to spy on someone either for legal or illegal purpose. (spywares such as keyloggers are installed by the owner of a shared, corporate, or public computer on purpose in order to secretly monitor other users)
Adware displays ads (generally in POP-UP’s form without your permission)

A Worm is a program which infects the computers which are connected by some network. Worms slow down the network. Worms are completely autonomous. They actively scan the internet for new targets, immediately infect them and the new target starts scanning the internet for new targets. Worms can spread extremely quickly because there is no need for human interaction. Nimda, Code Red and Blaster are famous examples of this.

A Trojan is a program which is usually hidden as a useful program, but can then be used by a hacker to take control of your computer. [Trojans are also known as Backdoors]. Trojan Horses are disguised to look like something useful but are actually malicious. Most trojan horses these days fall under one of the other categories because nobody writes random destructive code anymore. In the early days many viruses and trojan horses would do nothing more than delete your entire hard drive. Now, the virus writers want to make money by sending spam or collecting credit card numbers and marketing information.

Rick