The common use of the word logic says 'Something that makes sense'. In mathematics, logic is the study of true and false.
Logic uses operators to combine combinations of trues' and falses'.
AND Say to get a true outcome you need two variables to be true. We call the variables a and b. If an outcome only requires one of a number of variables to be true, we can say they are OR'ed. If we have 2 variables then if one other or both are true, the result is true. Normal language 'or' is actually an XOR, meaning one but only one.