Every day, we express opinions that we believe to be accurate because they're each based on a string of ideas that add up to a conclusion. Sometimes the point we're trying to prove doesn't track with rules of logic, so we wind up with a formal fallacy, also known as a logical fallacy.
Basically, formal fallacies are invalid arguments. The statements making up the argument may or may not be true; that's not the important part. It's all about drawing conclusions that don't follow logically from a series of statements.
Here is an example of an invalid argument that's false:
Some girls are born with blue hair.
Julie is a girl.
Therefore, Julie was born with blue hair.
Now, here's an example of an argument that's true, but invalid:
Some girls have long hair.
Amy is a girl.
Therefore Amy has long hair.
Both of these examples start out with statements about "some" girls, not all girls. You could safely assume that Julie might have been born with blue hair and that Amy might have long hair. But you couldn't know for sure by either series of statements.
To make the arguments valid, we could substitute the word "all" in the first statement. Of course, selling the case for blue-haired babies would still be pretty tough!