Your statement of purpose is essentially a mission statement for your PhD. Most applications will require you to write one as part of the application - but even if you do not need to do this, I urge you to do so as it will be a powerful motivational tool. Approx 400-500 words.
Source:
Personal Statements for PhD Study | FindAPhD.com
Make sure you check with the specific University and project you are applying for. But generally:
A brief description of what's led up to you doing a PhD.
What's your motivation for doing a PhD?
Don't simply list what's in your CV. But do explain the significance of the key areas in your CV and how they relate to your ability to pursue a PhD.
Any relevant experiences and awards that demonstrate your character and other qualities that will make you a suitable PhD candidate.
Any relevant work experience.