Formal writing is very distinct from informal writing.
Formal writing is less personal and more objective than informal writing.
It is also important to use formal grammar, which is:
...a set of rules of a specific kind, for forming strings in a formal language.
What makes writing formal (as opposed to informal) is the structure and tone used by the writer. One does not use slang, abbreviations, or colloquial English (which is familiar or informal conversation). In formal writing, the author should write in the third person (he, she, it, they, etc.), avoiding first person ("I"), or "you." Avoid terms such as "guy," "kid," "awesome," or "great." Words such as "children" or "excellent" would be more formal in nature.
Contractions should not be used. Instead of "wouldn't," write the word out: would not. "Won't" would be "will not," etc. Clichés should be avoided. A cliché is:
...an expression, idea, or element of an artistic work which has been overused to the point of losing its original meaning or effect, rendering it a stereotype, especially when at some earlier time it was considered meaningful or novel [new].
Examples of an abbreviation are:
"It was such a drag," "Love is blind," and "Misery loves company."
Abbreviations should not be used except in the case of titles. "TV" should be written as "television," but "Dr. John Smith" would be an appropriate abbreviation of "Doctor."
Sentence structure should be more sophisticated, varying the form used. Some sentences could start with prepositional phrases: "Around the bend, we saw a beautiful lake," as opposed to the more direct and informal, "We saw a beautiful lake around the bend." Another example is: "Because we were so late, we missed the opening speech." The more informal (and less interesting) form of this sentence would be: "We missed the opening speech because we were so late." Switching the word order around makes one's writing much more interesting.
The tone of the writing should be "business-like," avoiding any sense of familiarity or friendliness, which should be reserved for informal writing. That is not to say that one should not be congenial in tone, but one should not be writing with the style of a letter addressed to casual acquaintances or friends.
These are examples of structure one should use in formal writing.