The purpose is the change that you expect in the target group’s situation at the end of the project. It is the reason why your project was developed in the first place.
The scope of the project is defined by the purpose: who will benefit (how many people, what gender, age, social group); what is the time-frame; what is the area of intervention. Again, the relation between the purpose and the goal(s) is important: when the purpose is realised it should make an real contribution to achieving the goal. On the other hand, the purpose has to be realistic in view of the limitations of the project and of its participants (and their means), and in view of the context (risks, assumptions)
Generally, it is said that a project should only have one purpose, but in some cases projects can be so complex that they involve multiple purposes. In that case it is generally a good idea to split the project up in different individual projects, each with its own purpose.
A purpose (like a goal) is formulated like a state that is achieved, for instance: 'All children in the Tizandat district aged between 6 and 15 have access to basic education before 2015'.
When you formulate the purpose, make sure that it is realistic and achievable. Together, the outputs of the project should reasonably lead to the realisation of the purpose.