No, we're not talking about that Twain. The word "twain" actually means two. And convergence? That's when two things come together into one. Put that together, and you've got yourself—wait for it—two things coming together.
Wait, that's it? Well, yes, but the two things are none other than the infamous iceberg and Titanic. And since we're reading poetry, we're gonna bet there's something deeper going on here, too.
The speaker talks a lot about abstract things like an "Immanent Will" that drives creative and destructive forces together, so this convergence is one that's supposed to be a little ambiguous. That's why he doesn't say, "The Convergence of the Iceberg and Titanic." If he said it that way, we'd think he was just going to tell us about that famous crash once again. But instead he purposely leaves that "convergence" open for interpretation and gives us some space to contemplate things like creation and destruction in the context of this tragedy.
The convergence itself is what the speaker appears to be most interested in, whether he's considering an Immanent Will or "paths coincident." That tragic collision between man's most mega-supreme (at that time) symbol for vanity and luxury and nature's sinister iceberg appears to the speaker as two worlds colliding: man's pride and nature's "oh no you didn't" reality check. So this convergence is really a kind of metaphor for the kinds of things man might consider valuable and nature's silent awareness that luxurious things don't mean jack diddly squat at the bottom of the sea.