File Indexing is simply a service which helps in searching information from data on your hard drive which then creates a searchable keyword index! It extracts these information from your all your files located on the HDD. If you want to speed up your computer a little bit, I will advise you to disable File Indexing!
Follow the below procedure:
Open "My Computer"
Right Click on "Local Disk C:"
Click on "Properties"
Uncheck "Allow Indexing Service to index the disk for fast file searching"