Aims are what teachers (and learners) want to achieve in a lesson or a course. Activity in a class is planned in order to achieve these aims.
A lesson aim could be for the learners to demonstrate that they understand the form or use of the passive better, or to have practised intensive reading. A course aim could be to improve the report writing skills of a group of business students.
In the classroom
Aims on lesson plans often describe what the teacher wants learners to be able to do by the end of a lesson, or what they will have done during it. Teachers can tell learners their lesson aims, or involve learners in setting them. This can help create a sense of purpose and progress.