The title of this poem isn't a complete sentence. Wait, it isn't? (Checking…) No, it isn't. All we have is the phrase "when we two parted," which can't stand alone. Try writing it in a Word document and see what happens (put a period on the end as well). How about that—a writer not writing a complete sentence. Okay, that's being a little too harsh, because the sentence is incomplete for a reason—err, several reasons.
The most obvious reason is this little incomplete sentence piques our curiosity. We know something happened when so-and-so parted, but what? We have to read to find out. It's like coming home and smelling something good cooking and heading toward the kitchen to find out. Okay, well it's not that fun, but you get the idea.
Here's another thing about the title. It doesn't really tell us anything other than two people ("we") parted. That's it. As we read the poem, we discover a few more details (it was damp and chilly, the woman's kiss grew cold, the speaker is still upset), but, for the most part, many important details are left out (who parted from whom, what really happened, etc.). The title is vague in the same way as the poem, or rather the title foreshadows the vagueness and reticence of the poem. Thanks bunches, Lord B.
Now this vagueness and reticence were important. They may even have kept Byron out of trouble. He got into a lot of trouble as it was, so this would only have kept him from taking a dip in more hot water. The poem is partly an allusion to Byron's relationship with Lady Frances Wedderburn Webster, and partly an allusion to her relationship (affair) with the Duke of Wellington. You couldn't just write offensive stuff like this. People did, but it never really worked out for anybody if they tried it. Byron left out important details perhaps to keep himself from any more accusations and, perhaps, as a courtesy to Lady Frances, for whom he still had some affection. Head over to "In a Nutshell," where we fully dish the dirt.