What does curly brackets in the `var { ... } = ...` statements do?

What you're looking at is a destructuring assignment. It's a form of pattern matching like in Haskell.

Using destructuring assignment you can extract values from objects and arrays and assign them to newly declared variables using the object and array literal syntax. This makes code much more succinct.

For example:

var ascii = {
    a: 97,
    b: 98,
    c: 99
};

var {a, b, c} = ascii;

The above code is equivalent to:

var ascii = {
    a: 97,
    b: 98,
    c: 99
};

var a = ascii.a;
var b = ascii.b;
var c = ascii.c;

Similarly for arrays:

var ascii = [97, 98, 99];

var [a, b, c] = ascii;

This is equivalent to:

var ascii = [97, 98, 99];

var a = ascii[0];
var b = ascii[1];
var c = ascii[2];

You can also extract and rename an object property as follows:

var ascii = {
    a: 97,
    b: 98,
    c: 99
};

var {a: A, b: B, c: C} = ascii;

This is equivalent to:

var ascii = {
    a: 97,
    b: 98,
    c: 99
};

var A = ascii.a;
var B = ascii.b;
var C = ascii.c;

That's all there is to it.

They're both JavaScript 1.7 features. The first one is block-level variables:

let allows you to declare variables, limiting its scope to the block, statement, or expression on which it is used. This is unlike the var keyword, which defines a variable globally, or locally to an entire function regardless of block scope.

The second one is called destructuring:

Destructuring assignment makes it possible to extract data from arrays or objects using a syntax that mirrors the construction of array and object literals.
...
One particularly useful thing you can do with destructuring assignment is to read an entire structure in a single statement, although there are a number of interesting things you can do with them, as shown in the section full of examples that follows.

For those familiar with Python, it's similar to this syntax:

>>> a, (b, c) = (1, (2, 3))
>>> a, b, c
(1, 2, 3)

The first code chunk is shorthand for:

var {Hotkey: Hotkey} = require("sdk/hotkeys");
// Or
var Hotkey = require("sdk/hotkeys").Hotkey;

You can rewrite the second code chunk as:

let Cc = Components.classes;
let Ci = Components.interfaces;
let Cr = Components.results;
let Cu = Components.utils;