not operator

yeah I know it's a not operator but how does it relate to what's in the brackets. Does it mean return the inverse of the return value of the function in the brackets? I'm sure this is a stupid question but I don't get it.

In computing, we generally use the term brackets for [ and ] symbols, sometime soft brackets for { and } (also called braces). What I see above are more often called parentheses. The terms can vary, particularly from one country to the other, but these are the most common uses.

Anyway, yes. Evaluate the boolean expression between the parentheses, and just return the opposite.

Note that according to Boole (IIRC), the expression
!(left > otherRight || right < otherLeft || top > otherBottom || bottom < otherTop)
can be rewritten as
left <= otherRight && right >= otherLeft && top <= otherBottom && bottom >= otherTop