Watson's luggage is used as a distraction to assist Watson and Holmes in their escape. It will end up in Paris and has no further role in the story.
In "The Final Problem," Sherlock Holmes is locked in a dangerous battle of wits with the criminal mastermind, Professor Moriarty, whom Holmes himself appraises as the most dangerous adversary he has ever faced. Recognizing the threat Holmes poses and the danger he is in, Moriarty responds by seeking Holmes's destruction. Thus, already as the story begins, Moriarty and his agents are already in pursuit of Holmes, trying to assassinate him.
This is the context behind the elaborate instructions for the Baker Field escape as Watson and Holmes flee to the continent. Watson's luggage had previously been sent to the train ahead of them, but it is ultimately employed as a false trail for Moriarty to follow. Holmes and Watson disembark at Canterbury and travel onward by a different route. They leave the luggage behind, and it continues without them en route to Paris.