“Famous” means something (or very commonly, someone) is very well-known. The reason they are well known could be for good reasons or for bad reasons. “Notorious” also means well-known (and is most commonly again used to describe people) but is always for bad reasons. Elvis was a famous American musician. Hitler was the notorious dictator of Nazi Germany.

Famous means being well-known for a good reason and notorious means being well-known for a bad reason.

Both words indicate something that is well-known or widely recognized, but "notorious" is used to describe something negative. For example: Mc Donald's is famous for their delicious french fries. Mc Donald's is notorious for serving highly caloric meals.