You shouldn’t have to turn off your iPhone very often. If you’re not going to use it for a few hours, it’s not worth the hassle (and minuscule battery life savings) to shut it down.
But, if you know you’re not going to use your phone for a couple days, or on a very long international flight, and you want to save every last ounce of battery life, shutting it down can be an effective option.
Also, if you suspect some bug has made your phone unresponsive or slow, the first troubleshooting step should be that old IT standby: turn it off and on again.
You used to be able to force a restart on iPhone by holding down the side and Home button for awhile—10 seconds or so. With no Home button, you have to force a reset a little differently.