Essentially, formal communication is a type of communication that uses correct language, avoids slang entirely and keeps personal information to a minimum. If you write an email to your boss (known as ‘upward communication’ in the working world – how delightfully condescending of them!), then it is likely that you will be using formal communication.
Likewise, if you were to write a letter of complaint regarding, say, an inconsiderate neighbour or an unsatisfactory product, you would once again be using formal communication. If a lawyer writes to you, his/her letter will almost certainly be written formally.
Casual swearing (or any kind of swearing for that matter!), colloquialisms, personal anecdotes/questions and bad spoken habits (such as using the word ‘like’ as a form of punctuation, or ‘umming and ahhing’ too often) have no place in formal communication.
People communicating formally (as opposed to formicating communally, you understand), will also tend to use longer, perhaps more academic words and terms appropriate to the theatre of communication. If you work in marketing, for example, formal communication would see you using marketing-specific terminology at a far greater rate than you ever would in social situations.
The opposite of formal communication is ‘informal communication’. Informal communication would include the way you address friends and family, using first names instead of surnames and using a lot more slang words and opinionated speech.
When communicating formally, it is usually best to keep personal opinions to a minimum and, where possible, to discuss things from a third person perspective. Thus,
“I’ve been looking at these figures all night. So much so that I think I’ve gone cross-eyed! Anyway, I think its safe to say that the product isn’t selling”
“After careful evaluation of the figures, it is reasonable to assume that the product isn’t selling”
No personal involvement. No anecdote. Statistical data takes a greater role than personal opinion. See?
Of course, using informal communication in certain formal situations can be beneficial. Today, many corporations are employing informal language in order to better relate to customers and staff and corporate CEOs and motivational speakers tend to use informal communication as a way of maintaining a ‘man/woman of the people’ image.