While not the most complicated of topics to understand kiting, sometimes known as orb walking, A-Clicking, stutter stepping, etc, is a very important, and not easy, skill to master for all roles. Kiting is a skill most commonly used by the ADC but can be applied and adapted into other roles as well.
Because kiting isn’t the easiest concept to explain without visual representation I’m going to add a few videos to accompany the text. Hopefully this will help you understand better.
The most basic definition of kiting is being able to auto attack, walk, auto attack and continue the process. The goal of kiting is to be able to constantly deal damage while keeping yourself unharmed. In terms of champions who don’t auto attack, AP champions with short cooldowns usually, kiting can be accomplished by casting spells moving and casting again.
So when do you want to kite? Mostly always. Obviously If you’re in a 1v1 situation and you’re ahead enough to just run at the other person then that’s your call. However, if you’re in a team fight situation you cannot just run at the enemy. If you were to stand completely still in a fight you will be killed. That makes the concept of kiting especially important to the squishy targets, such as the ADCs and APCs who tend to be very squishy. Moving around greatly increases your chances of surviving as well as forcing you to be attentive to your situation.