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.

What should a statement of purpose include?

Source:

Personal Statements for PhD Study | FindAPhD.com

Make sure you check with the specific University and project you are applying for. But generally:

Your Background

A brief description of what's led up to you doing a PhD.

Why You Want to Do a PhD (or this specific PhD)

What's your motivation for doing a PhD?

Academic Experience

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.

Extra-Curricular Experience

Any relevant experiences and awards that demonstrate your character and other qualities that will make you a suitable PhD candidate.

Industry Experience

Any relevant work experience.