Spyware can also be called Trojans or malware. They can be downloaded by you, thinking it is something else, or by someone who has access to your phone. Once it is installed, it can track your cell phone activity, collect your personal information, and send it to a third party. It can even run up your cell phone bill by sending numerous text messages, or disable your phone altogether.
For more information on spy spyware, and how to protect yourself, see Does software exist that can spy on the contents of my mobile phone?