宣 xuān to proclaim

to proclaim; to declare; to announce

How it came to be

A roof over a spiral, a hall with a coiled pattern in the floor or ceiling. It was one particular palace building, where announcements were made.

宣布 (xuānbù) - to announce - is used for a formal, one-time declaration: 宣布结果 (xuānbù jiéguǒ) - announce the results.
宣传 (xuānchuán) - to publicize/promote - is an ongoing activity, and is neutral in Chinese (used for marketing and campaigns), unlike the negative connotation "propaganda" often carries in English.
宣誓 (xuānshì) - to swear an oath - is used for ceremonial pledges, e.g. taking office.
Formal, official register throughout; not used in casual speech.