so, would you clarify this like how CC is better than maven/Ant in this specific area?
You're still trying to compare grasshoppers with tree bark: they're two completely different things. CC isn't "better" than Maven/Ant. CC *uses* Maven/Ant.
Assume a team of a dozen people. Each person makes local changes and sends them upstream. The CI server says "Oh, look, a check in, I should to a build." The CI server pulls in the latest source, finds the build fails, and sends an email out. Or the build passes, the CI server generates Javadocs to a known location, runs code quality metrics and builds the report, whatever.
The point of a CI server is to merge developer code early, and often. A local box running Ant is only going to do that if the developer is highly motivated and disciplined. Which developers aren't. "Oh, I forgot to run that particular test suite." "Oh, my code interacts poorly with your code but I hadn't run locally with a completely updated source tree."
Search the web for "continuous integration". *That's* what a CI server does, and it's nothing like what Ant/Maven do.