.part means only part of the file has downloaded. When I use Firefox to download files it generates .part until the whole file is downloaded and the .part disappears. If you are downloading from Apple's web site the only thing I can suggest is you try again. A downloading issue through a browser isn't really an iTunes issue. If you are not using a browser to download I would suggest you do as sometimes installing from a stand-alone updater works better than any automated method.
You may also wish to read the links below if you are still having problems:
Apr. 2015 Niel post: Re-install iTunes application - https://discussions.apple.com/thread/6990002?answerId=28055467022#28055467022 - delete the old application first, with instructions on how to do that.
A similar technique by Ben.d using Terminal to delete the application - https://discussions.apple.com/thread/6985231?answerId=28036630022#28036630022 Normally you don't have to delete an old application but this time it seems to be necessary for some.