I was being a good husband and updated my wife's iPad to iOS 9 last night. This morning I wondered why she didn't get up at her usual time and I had to go wake her so we could go to work and get the kids to school on time. Turns out the update to iOS 9 didn't complete and got stuck with a message on the iPad lock screen of "slide to upgrade." Oh yeah, she uses her iPad as her alarm clock, so that didn't work out so well for her this morning.
So your iOS device didn't quite finish the update or install of iOS 9. Now what? Turns out you are not alone. Apple has even written a support article. Read Apple's 3 step process. However, there is one aspect of this process that Apple doesn't really explain.
Your device is essentially in "limbo." It doesn't have a complete a fully operational operating system installed. This is a bit of a problem because in order to make any significant changes to your device you have to not only unlock it, but also turn off the activation lock (i.e. "Find My iPhone"). There is a way around this. This is what step 2 in Apple's fix is helping you get around. By holding down the power and home buttons at the same time for 10 seconds you are putting your iOS device into what is called DFU mode, which stands for Device Firmware Update mode. By doing this you can reset your iOS device to factory settings, but only if you enter in the Apple ID and password that was used to activation lock (or turn on "Find My iPhone"). This ensures that you are the rightful owner of the device. Because your device is "activation locked", this mode is the only way you can wipe the device and reload iOS and fix the failed install problem.
Hopefully the steps I described from Apple's support article resolve your iOS 9 upgrade issues, because they did not work for me. My wife's iPad is still stuck in the "slide to upgrade" loop even after going into DFU mode and updating that way. We called Apple and they walked us through the same process I described above and it didn't work then either. Apple has now directed us to take the iPad into the Genius Bar at Apple and have someone try and resolve the issue in person. So if these steps didn't work for you it looks like you may be making a trip into an Apple Store or an Apple Certified repair center.
My wife's iPad is a 4th generation iPad, the iPad just before the iPad Air. I upgraded my iPad Air to iOS 9 and had no issues. This issue is more common with older devices.