The iPhone uses plenty of motion effects when the Home Screen is tilted, or when apps are opened or closed. Leaving this on can run down the battery and has led to some reports of motion sickness.
To stop this, open Settings, then select General, followed by Accessibility. From here, select Reduce Motion and turn the option on.
When it’s turned on, you also get the option to disable Auto-Play Message Effects. Turn this off if you don’t want to see the full-screen animations that can be sent in Messages.