What does this mean in an If statement?

The way that if statements work is that they takes a conditional statement and either execute the following block of code if the condition is true, or skip it if the condition is false.

So essentially you could say if true then and it would always execute the code block. Same goes for if false then, except it would never execute the code block. All that is required for the if statement condition is that it evaluates to a boolean (true/false) value.

Following BlackJPI's explanation, not x evaluates to true if and only if x is neither nil or false. Since nil represents a lack of useful value (nothing), you can use this to test whether a value exists.

So if not gameThing and gui.Visible then would mean if gameThing exists (and is not explicitly false) and gui is Visible then do the following.