The word 'purpose' normally means 'what you want to do', however, it has a secondary meaning, which is the quality of knowing 'that you want to do something'. Purpose in this sense means having a direction, and it is essential that your statement of purpose shows that you do have a direction and know both where you are going and how you can best get there. A good statement of purpose will usually have the following structure:
YOUR PAST
How your studies at undergaduate level and at graduate level, as well as any other work or study experience, has prepared you for the course of study that you wish to take.
YOUR PROPOSED COURSE OF STUDY
Should be shown to be a logical follow-on from your studies/work to date and to prepare you for your future career.
YOUR FUTURE CAREER
Should be something for which your proposed course of study is valuable or essential, and should have some logical connection to what went before.
Of course, you own career may not be as simple as this. Perhaps you started studying biophysics, then later developed a passion for medieval poetry. This is not going to disqualify you, but you need to ask yourself 'why should a university choose me rather that someone who has always been interested in medieval poetry?' If you can answer this question, you have a chance of being considered. If, however, your reader gets the impression have suddenly for no good reason conceived an interest in a field you have never studied before, they may equally assume you will lose interest just as quickly. You best chance usually lies in showing that there is a meaningful progression to your career which is driven by your sense of purpose and academic or professional ambition.
The above model suggests that a statement of purpose should move from your past and present studies, to your proposed studies and finally to your future career. If you want to be innovative, you are not obliged to follow this pattern, but the elements and the connection should be there and should be clear to the reader. Before you start writing, draw yourself a clear structural plan, perhaps allowing a paragraph or so for each stage. Obviously, your past will be much clearer and more detailed than your future, but don't neglect the second and third boxes in the diagram above, or you may look like an eternal student, always hunting for something new to study.