If we re-write the paragraph it becomes clearer: The teachers of these subjects did not appeal to my curious 'and' active mind. The result was that I did not really work at them and so 'remembered' only what stuck from repetition the barest rudiments of a school education. - Here stuck means 'remembered' - only through repetition did any of the things taught 'stick to' or 'stay in' the persons head/brain/memory.