A Statement of Purpose is a letter you write about the purpose behind your PhD application. All schools ask for a Statement of Purpose (some may call it by some other name), and many consider it one of the most important aspects of your application (but some schools seem to not even read it).
Schools usually don't provide much guidance about how that statement should be. And, please, don't use templates you find in the internet. A statement of purpose is your statement, with your style, with your way of thinking, your purpose. You can't do that if you copy someone else's.
Your statement should not be too long. I'd say about 1,000 words, 1 or 1,5 page. And believe me, it can be a real challenge to write all you want in such a short text. You may have a lot you want to tell the school. At least I did. But it didn't fit in 1,000 words. I think one of the things you are being tested here is if you can write a very short text which will cause a big impact. You should be focused, concice, but powerful. Because that's the way you are expected to write papers during your PhD. They don't want to see people rambling endlessly. I started with a long text with everything I wanted to write, and then improved it several times.
Your statement should also be very tailored to PhD applications. When you apply to MBA, for example, you are expected to write a lot about your career, professional results and achievements, extracurricular activities. You can also write about the challenges you faced in life, how you struggle but ended victorious. But, for PhD, if a school want to know about those things, they will give you the chance of writing another letter, like a personal history statement. The Statement of Purpose for PhD applications are much more related to your potential as an academic researcher in the concentration you chose and how you would fit into the program you're applying.
As the name says, you should state what is your purpose. That purpose may come from a professional experience, or a life experience, or any other thing like that. But it's not your experience by itself which is important, but how that experience explains your motivation to do research.
I started my Statement of Purpose with the general purpose I have for my career from this time on: "to discover and develop measurements for Marketing results (particularly metrics related to Finance) and to lead much-needed changes in business and education in my country".
Then, I explained what led me to that purpose. I wrote about the difficulties I had when working in corporate finance, when I was not able to decide and analyze marketing investments and budgets. How I came to the personal conclusion that one of the most importants ways to achieve the great goal of Corporate Finance of maximizing shareholder value was to maximize consumer value. But had no ways to understand that in a clearer and deeper way. Showed that my master's thesis and consequent paper presentation was a first step in that direction, but it was not enough, as I could not answer many questions by myself. Questions that have become almost an obsession for many years.
I explained about the precarious situation of business management and education in Brazil. And how I though that improving education was the way to get out of the chaos my country constantly faces. So, inspiring people through education was very important to me, and one of the best ways in to become a great academic.
So, a PhD looked like the natural next step in my life. There was a time to acquire knowledge (undergrad and MBA), a time to turn knowledge into action (20 years of professional career), a time to spread knowledge (5 years of teaching experience), and a time to question the knowledge I thought I had (my master's main consequence). It's time to generate new knowledge, it's time for my PhD.
That part of my Statement of Purpose was basically the same for all schools I applied to. But that doesn't mean my whole statement was the same for all schools. You should write a different statement for every school you apply to.
The main reason I say it is that you are not only expected to explain "Why a PhD?" or "Why now?" (which are general questions), but also, for example, "Why this university?" (whose answer is different for each school).
If you did your research about schools and faculty like I suggested in my previous post, this shouldn't be too hard. Because you know the schools, you know the faculty, you know what they are researching. In your statement of purpose, show that that you know why that specific PhD program is the best fit for your own purpose stated before. Now is a good time to read those papers more carefully, to write in a more refined way how your research interests mirror or complement the interests of the school or of a specific professor.
You should convince a school that you are really interested in the university, the program, and the faculty's research. And that interest comes from a understanding about them, and a match with your purposes and research interests.
If you mention a professor in your statement of purpose, it increases the chances that that professor will evaluate your profile and then interview you (if he/she likes your application, of course). And it's a lot easier to be interviewed by someone whose work you know and who have similar interests, than to be interviewed by someone who you know nothing at all. You can also mention and briefly discuss a relevant paper you read.