I think informal english is related with the way you talk to someone depending on the relation you have.
For example. If you are having a conversation with a friend or parents, you may use phrases like What's up? or Hey Buddy. I think you wouldn't use these expressions with your boss, instead you would say thinks like "Hello, Sir or How are you today"?. Informal english is less polite than formal english.
I am sure that every language has different "registers" or levels of formality.
The English you learn in a classroom is English you can use anywhere--in speaking, in writing, with friends, in a job interview. The worst that can happen is that people will say (as they often do) "Foreigners always speak better English than we do."
You need to be careful with informal English because you can use it in some situations, but not others. Therefore, it is important to know which words and phrases are "standard English" and which are "informal" or "colloquial" or "slang."
In English, depending to whom we are speaking with, you can choose between "informal" and "formal" English. This is often done to denote a level of respect. If you were talking to a friend, you may choose to say, "Whats up, Sup, Yo, Hey homie, ect..." However, if you were speaking with an authority figure (boss, police officer, professor) you would usually address them "Hello (insert title)" So "Hello, Dr. Jones" or "Good evening Mr. Matthews." In the Southern region of America, we also like saying "Yes/No ma'am and Yes/No Sir"
Hope this helps!