Hi Kenneth,
Welcome to the Microsoft Windows 8 Family! We are happy to assist you with your query on the Microsoft Community Forums.
As per the description, you would like to know about the Bonjour software from Apple, Inc. and also would like to know if it is safe to remove it from the computer.
Bonjour is a software that comes built-in with Apple's OS X and iOS operating systems and it provides a general method for the applications to discover shared services on a local area network, printer discovery wizard, and IE plug-in for discovering local Web servers. It allows the users to set up a network without any configuration.
It can also be installed onto computers running Microsoft Windows. It may be included within other software such as iTunes and Safari. The iTunes that might be installed in your uses Bonjour to find shared music, iPhoto to find shared photos, iChat, etc.
If you didn't install Bonjour for Windows manually, the most likely reason is that it was installed by an application that relies on Bonjour functionality.
You can definitely uninstall the Bonjour service without doing any harm to the computer. But, uninstalling or disabling the Bonjour service may limit the functionality of programs that use Bonjour.
Follow these steps to uninstall the Bonjour Application from the computer:
A. Press “Windows Logo” + “R” and type “appwiz.cpl” in the run command box and press “Enter”.
B. Search for the Bonjour application from the program list in the “Programs & Features” window.
C. Click on the Bonjour application and click on “Uninstall”.
D. Follow the on-screen instructions to complete the uninstallation.
You may find more details about this program from the link:
http://support.apple.com/kb/HT2250
Hope this is helpful. If you still have any issue or query with it, I would suggest you to contact the Apple Support from the link:
http://www.apple.com/support/contact/
Thank you.