Indexing service is a service that indexes your files on your computer. It will read the meta data off the file and index it, thus theoretically making your future searches faster and more effecient.
It is kind of poorly coded on the windows platform, and you can disable it by going into start > Control Panels > Administrative Tools > Applications and Services > Services > scroll down and find and disable Indexing service.
Typically it is suppose to run in the background when your computer is idle, but it doesn't always do that. You probably started it by checking the box in windows which says something like, do you want to make these searches faster in the future? If you click yes, it turns on indexing. By default, that service is disabled.