Gradle is to the Groovy JVM language what ant is to Java. Basically, it's Groovy's build tool. Unlike Ant, it's based on the full Groovy language. You can, for example, write Groovy script code in the Gradle script to do something rather than relying on a specific domain language.
I don't know IntelliJ's specific integration, but imagine you could "extend" Groovy such that you could write specific "build" language primitives and they just became part of the Groovy language. (Groovy's metaprogramming is a whole discussion unto itself.) IntelliJ/Google could use Gradle to build a very high-level build language, yet, it's a language build on an expandable, open standard.