Although not an officially documented change in iOS 10.3, one Apple engineer revealed that some of the animations, including how apps appear when they're launched and exited, have been streamlined and shortened in such a way that you may notice things feeling a bit "snappier" as you navigate from app to app.
Additionally, the rollout introduces a major update that will be seemingly invisible to users: a new and more efficient file system for iPhones and iPads. Without getting too technical, this new system improves the read and write speeds for your device, allowing it to save and access data via apps more quickly, reduce lag, and potentially cut down on frame drops and keep things running more smoothly overall. However, because it's such a fundamental change to how iOS operates, the 10.3 update will take slightly longer to install, so just make sure you give yourself a little extra time for it to run its course. If you haven't been prompted to update already, head to Settings > General > Software Update and pull the trigger.