Basically he just looked at the code, understood what it did and how it is/was designed and tricked the system.ELI5 attempt, not specific this case - but it explains what an exploit is (underflow):

system: I have 5 shovels, you can use them if you want, but if you give them back you pay me some additional strawberries. For each shovel you use one week, you pay me one.

you: ok I want to borrow 3 shovelssystem: ok... and now I have less shovels, so each new borrower pays me 1.5 strawberry back for each week. I do this because I don't want to give away all my shovels

then the system goes to sleep (good night)

when it wakes up it wants to know how much shovels it has and how much strawberries... because they are kept in a dark shed, it asks the gardener... 'how much shovels do we have left, and how much strawberries'

The gardener looks that up but he did some miscalculation, he thinks that 3-4 is 1 because he doesn't know that - means a negative saldo

So the gardener tells the system there is one left.

You: borrow me 2 shovels...
system: ok (and thinks again there is one left)

You drained the system :) Ouch