To diminish is to make less or cause to appear less. In music it is used in several different places, the musical term diminuendo means to lessen in force, or gradually get softer or quieter in tone.
It also means to make an interval smaller by lowering the top note half a tone, or in the case of a piano playing one key to the left of the original one.
So, what's the "Return" for learning about diminish in the Moonlight Sonata- What's in it for you?
The hardest measures for a novice to read are the ones with the extra sharp and double sharps in them. If you learn how to play it outside of the piece of music, you will be able to play the passage with ease.
Learn diminished patterns before playing them in the piece. It will save you lots of time and effort. You can see an explanation video here.