They made the most of the last few hours in which they were allowed to do magic before the holidays. They played Exploding Snap, set off the very last of ...
"They made the most of the last few hours" sounds like an incomplete statement. I have gone through the definitions of the word "make" to get one that can fit for this context, but none of them seems to suit. What sense of 'make' has been applied in this sentence?
-- From Harry Potter.
It is an idiomatic expression:
to use or enjoy something as much as possible:
- We’re only in Paris for a day, so let’s make the most of it.
Surely this is an example definition 3a, not 2a:
to bring into being by forming, shaping, or altering material
The sense of the word here is that something -- say time -- is an essential ingredient for things that are good (enjoyment, accomplishment, friendship, etc.) and so you've "made the most" of time by maximizing your enjoyment, accomplishments, etc.
"Waste" is an exact antonym of "make the most of" in this sense, and note definition 3a of "make" is opposed to the meaning of the word "waste". Contrast:
I made the most of my time in college
I wasted my time in college
I made the most of my budget
I wasted my budget
I have made the most of my talents
I have wasted my talents
to cause to happen to or be experienced by someone
Playing Exploding Snap, etc. is something that they experienced. They made that happen. The word "of" introduces an indirect object that in this context indicates what the direct object was from. To make X of Y means to use Y to cause X (often, "make" takes the double preposition "out of": "make a coat out of fur", but in this context "of" is sufficient). They used the last few hours to make playing Exploding Snap, etc. happen. So playing Exploding Snap, etc. is something they made of the last few hours. Presumably, playing Exploding Snap, etc. was the most they could make of the last few hours.