when a large corporation contacts you with the direct instructions to stop doing something and not do it again. generally because they have legal rights to object you are copying or distributing.
A legal term literally meaning, "stop what(ever) your doing and don't do it again." Hence, "cease" meaning to "stop," and "desist" meaning to "not do again in the future."
Usually used by a person or party against another person or party when they are doing something that they find: offensive, strange, violating, embarrassing, shady, etc.