In Java, it means nothing.
But that comment says that the line is specifically for GWT, which is a way to compile Java to JavaScript.
In JavaScript, integers are kind of like doubles-that-act-as-integers. They have a max value of 2^53, for instance. But bitwise operators treat numbers as if they're 32-bit, which is exactly what you want in this code. In other words, ~~hash says "treat hash as a 32-bit number" in JavaScript. Specifically, it discards all but the bottom 32 bits (since the bitwise ~ operators only looks at the bottom 32 bits), which is identical to how Java's overflow works.
If you didn't have that, the hash code of the object would be different depending on whether it's evaluated in Java-land or in JavaScript land (via a GWT compilation).