Typically used in careful, edited writing — when the writer has a lot of time to polish his text. Formal English also occurs in speech, usually when the speaker is saying something that was prepared beforehand (for example, reading the news or delivering an official speech).
Sentences are longer and more complicated, for example: Toyota’s US sales bounced back in March as substantial discounts helped to win back customers who had been shaken by the firm’s mass safety recalls.
The standard of correctness is higher. Some phrases are considered correct (or at least acceptable) in informal English, but wrong in formal English. For example:
I have made less mistakes. (formal: I have made fewer mistakes.)
She’s liking it. (formal: She likes it.)
I feel real good. (formal: I feel really good.)