What is the meaning of "Lan" (curse/damnation), and what is intended by it when it is said: "The Messenger of Allah, peace be upon him, cursed whoever did such and such"?

The implication of the phrase "The Messenger of Allah cursed whoever did such-and-such" is that this action is heinous, forbidden, and one of the major sins. This is because one of the criteria for a major sin is that a threat or a curse is attached to its commission.