To demote someone is to move them into a less important job. Your coffee shop boss might demote you to wiping tables if your attempts to froth milk and pull espresso shots continuously fail.
When your employer demotes you, she assigns you an easier task or even an entirely new, lower-ranked position. You may even earn less money. In the military, to demote is to move a soldier down in rank, usually as a punishment. The opposite of demote is promote, which came first. The prefix de- gives the word a sense of "down" or "down from."