United Kingdom and Ireland
At the universities of Dublin, Oxford and Cambridge, and at Westminster School, St Paul's School, London, Eton College, Winchester College, Harrow School, and various other UK educational establishments, an exhibition is a financial award or grant to an individual student, normally on grounds of merit (at Oxford and Cambridge, for example, it is typical to be awarded an exhibition for first-class performance in examinations). The amount is less than a scholarship.
In 1873 Annie Rogers come top in Oxford's examinations and she was automatically qualified for an exhibition at Balliol or Worcester College, Oxford. She was denied the place because she was female. As a consolation prize she was given six volumes of Homer and her place was given to the boy who had come sixth in the tests.
An exhibitioner is a student who has been awarded an exhibition (as a scholar, in this context, is one who has been awarded a scholarship).
In Australia, an exhibition is awarded to the student achieving the highest mark in a given subject among all matriculating students (i.e. those graduating from high school) in each state in a given school year.