This is called a boot loop and sadly there's not much you can do that doesn't result in you erasing the phone. Here's how to fix it if you have a Mac or PC, note that this will erase everything on the phone but if you have an iCloud backup of it, you'll be fine.
- Hold the power button, and both the volume buttons at the same time until you see the recovery mode screen
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- Plug the phone into a mac
- Go to finder and the iPhone should be in the sidebar
- select it and follow the instructions on the screen to fix it
- It'll tell you to either restore from backup or set it up as a new phone. You'll want to restore from backup unless you don't have a backup.
- after it's done, it should work well as new!
