In the age of iPhones and other rather pretty good phone cameras, it is tempting to use one of those photos that a friend or a family member took as your professional headshot that you plan to use for your professional life. If it works for you, go ahead. Many a times, it probably won't and that's when you need a professional headshot. What is a professional setting? Let's say anything that is not social or anything that is related to your job or profession.
LinkedIn is probably the most relevant platform for professional headshots but the use of a professional headshot could be in so many places and for so many different purposes that it is difficult to enumerate. Let's say you are going on a conference to speak and the organizers need a photo of you and/or a photo that will be on your company's website will most likely require a professional headshot. If you are self-employed, then for promoting yourself should almost always require a professional headshot.
So, what constitutes a professional headshot? Simply put, a photo taken by a professional photographer in a setting where there are proper background and lighting. While professional camera gears should also be present, most importantly it is the overall appearance, e.g. focus/clarity, color balance, resolution, and posing, of a photo that dictates what a professional photo is.
It is possible to create a professional looking photo with the iPhones of the world. Nothing wrong in that if that serves your purpose. But most often, it may not have the appearance of the brand that you are trying to create for yourself.