"To complete the update" means to finish or finalize the process of making necessary changes or improvements to something, such as software, a device, or data. Full definition
It is a brand new book with fresh ideas and complete updates for 2015. (MostenMediation.com)
Thus, after completing the update process you can start customizing the Android system and you can also consider in improving the performances. (android.gs)
I checked the software release, and it's still an older one, so whatever it's doing or not doing, it has not completed an update of any kind. (goodereader.com)