formal

Formal describes something that follows rules, is a dressy or important occasion, or something that has official sanctioning or approval. (adjective)

An example of formal is a dinner party at a mansion where everyone dresses up in fancy clothes and is very polite.
An example of formal is when a judge gives official approval of something.

See formal in Webster's New World College Dictionary

adjective

of external form or structure, rather than nature or content
of the internal form; relating to the intrinsic or essential character or nature
of or according to prescribed or fixed customs, rules, ceremonies, etc.: a formal wedding
1. having the appearance of being suitable, correct, etc., but not really so
2. stiff in manner; not warm or relaxed
1. designed for use or wear at ceremonies, elaborate parties, etc.: formal dress
2. requiring clothes of this kind: a formal dance
done or made in orderly, regular fashion; methodical
very regular or orderly in arrangement, pattern, etc.; rigidly symmetrical: a formal garden
done or made according to the forms that make explicit, definite, valid, etc.: a formal contract
designating education in schools, colleges, etc.
designating or of the level of language usage characterized by expanded vocabulary, complete syntactic constructions, complex sentences, etc.

noun

See formal in American Heritage Dictionary 4

(fôrˈməl)

adjective

a. Relating to or involving outward form or structure.
b. Being or relating to essential form or constitution: a formal principle.
a. Following or being in accord with accepted forms, conventions, or regulations: had little formal education; went to a formal party.
b. Executed, carried out, or done in proper or regular form: a formal reprimand; a formal document.
a. Characterized by strict or meticulous observation of forms; methodical: very formal in their business transactions.
b. Stiffly ceremonious: a formal manner; a formal greeting; a formal bow to the monarch.
Having the outward appearance but lacking in substance: a formal requirement that is usually ignored.