To demote someone is to move them down at work or in an organisation: a lower rank, a smaller job, less power. The army does it; companies do it. Schools almost never do it to children, so learners mostly meet it in news and office English. It is the opposite of promote. You demote a person (not, in the home meaning, a thing). It can be a punishment after a mistake, or a quiet change of roles. Formal; in talk people also say “they moved him down.” Though actually, writers sometimes stretch it for anything made less important (“the story was demoted to page 12”), but the first meaning is rank. Being demoted is not the same as being fired — you still have a job, only a lower one.

降職、降級