Spyware (also known as Adware or Malware) is a vague term generally referring to software that is secretly installed on a user's computer that gathers and reports personal information through the user's internet connection.
The term Spyware now covers a wide range of software that perform very different functions. These functions can include:
Yes, viruses essentially send themselves around and include the code necessary to reproduce as part of their contents. Spyware however is reproduced through web content (such as downloads) or other programs that users run on their machines (usually without their knowledge or consent).
Spyware can come from many sources, it is a common myth that you mainly get spyware from visiting adult related sites. Spyware can come from numerous places, the main places being websites of questionable integrity, file sharing networks and CD/DVDs. A good example would be Kazza, where Spyware is bundled into the installer. In this case, the user is informed of the contents in the agreement, but many users simply click "I accept" without reading the full agreement.