That explains it pretty well. If you don't get it, try looking at some truth tables:
NOT: The NOT operator accepts one input. If that input is TRUE, it returns FALSE, and if that input is FALSE, it returns TRUE. For example, NOT (1) evalutes to 0, and NOT (0) evalutes to 1. NOT (any number but zero) evaluates to 0. In C NOT is written as !. NOT is evaluated prior to both AND and OR.
AND: This is another important command. AND returns TRUE if both inputs are TRUE (if 'this' AND 'that' are true). (1) AND (0) would evaluate to zero because one of the inputs is false (both must be TRUE for it to evaluate to TRUE). (1) AND (1) evaluates to 1. (any number but 0) AND (0) evaluates to 0. The AND operator is written && in C. Do not be confused by thinking it checks equality between numbers: it does not. Keep in mind that the AND operator is evaluated before the OR operator.
OR: Very useful is the OR statement! If either (or both) of the two values it checks are TRUE then it returns TRUE. For example, (1) OR (0) evaluates to 1. (0) OR (0) evaluates to 0. The OR is written as || in C. Those are the pipe characters. On your keyboard, they may look like a stretched colon. On my computer the pipe shares its key with \. Keep in mind that OR will be evaluated after AND.