The purpose is the problem you are solving in your project.
On a display board, it can be stated in the background information section or the introduction.
This is an example of a purpose statement "To find out how table salt affects the boiling temperature of water." (http://www.isd77.k12.mn.us/resources/cf/ExmSciProj.html
A more advanced purpose statement is "The purpose of this project is to overcome the limitations of current neural network chips which generally have poor reconfigurability, and lack parameters for efficient learning." (http://www.virtualsciencefair.org/2006/stag6m2/
You can see more examples of science projects at: http://www.juliantrubin.com/sciencefairprojectsaz.html
Here are some other links:
http://www.sciencebuddies.org/mentoring ... oard.shtml
Good Luck with your project.