"Everything that Rises Must Converge": way to mystify things, O'Connor. Let's take a look at a few pieces of evidence to try to hammer some meaning out of this bizarre title:
The driving force that sets the story in motion is that Julian's mother must keep her blood pressure low—as in, it can't rise!
Julian's mother says that blacks "should rise, yes, but on their own side of the fence" (24).
All the characters converge on the bus.
At the end of the story, all four of the main characters rise to get off at the same stop.
The final encounter could be seen as a type of convergence—the black woman's fist converges with some part of Julian's mother.
Let's take these one at a time.
In the end, Julian's mom's blood pressure does rise, and it causes some sort of stroke. We can see this, maybe, as being a statement about consequences. Julian sees the attack as a harmless lesson, but in fact it's not harmless at all. There's no peaceful way to teach people a lesson, if their entire identity is wrapped up in a rapidly outdated truth.
Julian's mom believes in the "separate but equal" doctrine. The title "Everything That Rises Must Converge" undercuts that whole idea. African-Americans are "rising"—and they're going to eventually rise so high that they'll just leap on over the fence and "converge" with the white people. What Julian's mom doesn't see is that there's no way to rise without converging.
And that convergence is already happening: all the characters converge on the bus, and we see that blacks and whites aren't so different after all. They even have the same taste in hats.
If you really wanted to push the analysis, you could say that the "rising" to get off the bus and the "converging" at the same destination is a clue to the fact that we all want the same things out of life—just like Julian's mom and Carver's mom just want the best for their boys, but might not know the best way to go about it.
And, yeah. Sometimes, convergence is violent. In fact, it sounds a lot more like a clash than a neutral convergence.
In the end, we don't know if we should take the title as a warning, a statement of fact, or an optimistic promise. Pretty cool, right?