Half a year has passed since Apple released iOS 7. That seems like so long ago. Millions of crashes later, Apple has finally gotten around to releasing iOS 7.1. The biggest feature in the update is what it omits: namely, the resprings that happen randomly. Those are the mini crashes that make the device feel unstable. The problem was mostly felt by those with new devices sporting the A7 chip. I have been using some version of this update on my iPhone for a few months. I have had no crashes since that time.
There are a lot of little things in the update, most of which you will likely not notice. I suspect most people will notice a little extra snappiness to the OS. It was already fast. Things seem to zip along even faster.
You will want to go to Settings, General, Software Updates. It is a big update, so don't be surprised if it tells you that you don't have enough space. You might have to clear out a few things to make room. Enjoy.