What the teacher wants to achieve in the lesson or in the course.
The main aim is the most important aim; e.g. the teacher's main aim in a lesson could be to teach the present perfect simple or develop listening skills.
A stage aim is the aim or purpose of a stage, step or short section of a lesson, e.g. to provide controlled practice of the present perfect simple or to develop listening for gist.
A subsidiary aim is the secondary focus of the lesson, less important than the main aim. It could be the language or skills learners use in order to achieve the main aim of the lesson, or a skill or language area which is practised while the teacher is working on achieving the main lesson aim.
A personal aim is what the teacher would like to improve in his/her teaching, e.g. to reduce the time I spend writing on the whiteboard.