What does institution conferring award mean?

'Institution' can be a University, College, or School.

'Conferring' means to give.

'Award' is the certificate that if given to the recipient by that institution.

So ; if you went to a University you would write as the answer to institution conferring award ; ' University of ...., conferred a Degree of Batchelor of Arts.

In short , say 'Oxford' BA ( literature).