What is "function*" in JavaScript?

It's a Generator function.

Generators are functions which can be exited and later re-entered. Their context (variable bindings) will be saved across re-entrances.

Calling a generator function does not execute its body immediately; an iterator object for the function is returned instead. When the iterator's next() method is called, the generator function's body is executed until the first yield expression, which specifies the value to be returned from the iterator or, with yield*, delegates to another generator function.

Historical note:

It's a proposed syntax for EcmaScript.next.

Dave Herman of Mozilla gave a talk about EcmaScript.next. At 30:15 he talks about generators.

Earlier, he explains how Mozilla is experimentally implementing proposed language changes to help steer the committee. Dave works closely with Brendan Eich, Mozilla's CTO (I think), and the original JavaScript designer.

You can find more detail on the EcmaScript working group wiki: http://wiki.ecmascript.org/doku.php?id=harmony:generators

The working group (TC-39) has general agreement that EcmaScript.next should have some kind of generator iterator proposal, but this is not final.

You shouldn't rely on this showing up without changes in the next version of the language, and even if it doesn't change, it probably won't show up widely in other browsers for a while.

Overview

First-class coroutines, represented as objects encapsulating suspended execution contexts (i.e., function activations). Prior art: Python, Icon, Lua, Scheme, Smalltalk.

Examples

The “infinite” sequence of Fibonacci numbers (notwithstanding behavior around 2⁵³):

function* fibonacci() {
    let [prev, curr] = [0, 1];
    for (;;) {
        [prev, curr] = [curr, prev + curr];
        yield curr;
    }
}

Generators can be iterated over in loops:

for (n of fibonacci()) {
    // truncate the sequence at 1000
    if (n > 1000)
        break;
    print(n);
}

Generators are iterators:

let seq = fibonacci();
print(seq.next()); // 1
print(seq.next()); // 2
print(seq.next()); // 3
print(seq.next()); // 5
print(seq.next()); // 8

It's a generator function - and it said so in the page you cite, in the comment you replaced with "this is the interesting line"...

Basically it's a way to specify sequences programmatically so that they can be passed around and elements accessed by index without having to compute the entire sequence (possibly infinite in size) beforehand.

The function* type looks like it acts as a generator function for processes that can be iterated. C# has a feature like this using "yield return" see 1 and see 2

Essentially this returns each value one by one to whatever is iterating this function, which is why their use case shows it in a foreach style loop.