What does spyware and malware mean?

Malware is a malicious software like virus,worms etc. Spyware is also a kind of malware which acts as a spy , collects information about users without their knowledge

Malware, short for malicious software, is software designed to infiltrate a computer system without the owner's informed consent. It can damage your computer or perform malicious task on your computer without your knowledge. Malware includes adware, spyware, tracking cookies and infectors (worms, viruses, Trojans, backdoors, toolkits). Learn more at Wikipedia.

Spyware is tracking software that hides itself (runs in the background) and gathers the activity performed on a computer without the computer owner's or user's knowledge. These are used to spy on some one either for legal or illegal purpose. Learn more at Wikipedia.
Example:- HuntBar, Zlob trojan, etc.