That's called a Hard Reset. You do it when the device "locks up". This could be caused by a software fault, improper shutdown...anything. I've never had to do it on my IP4S.
It's not a bad idea to periodically (once a week/once a month) reboot your phone by holding the Power/Sleep-Awake button, then swipe and shutdown, then hold it again and let it start up. It's a computer; sometimes it builds up little errors and memory problems, and needs to be shutdown and rebooted to clear stuff out.
Also, it's a good idea to not let the phone battery run down to zero. Better to make a habit of putting it on charge at 20%.
After letting it charge a while, try pressing the Home button and the Sleep/Awake button at the same time (hold for 10 seconds, then let go and wait).
My Iphone 4s shutdown and I can't get it to turn back on. It was charged so the battery life was good. I have it charging now just to see what happens. It has been on the charger for an hour and still nothing. And my bill is current so it is not due to outstanding payment. I only have my cell phone and do not have a land line so I cannot call Sprint for help.