What is a simple explanation of higher order functions and callbacks in JavaScript?

http://www.quora.com/What-is-a-simple-explanation-of-higher-order-functions-and-callbacks-in-JavaScript

var animals = [

  { name: 'Waffles',  type: 'dog', age: 12 },

  { name: 'Fluffy',   type: 'cat', age: 14 },

  { name: 'Spelunky', type: 'dog', age: 4 },

  { name: 'Hank',     type: 'dog', age: 11 },

];

var oldDogs = animals.filter(function(animal) {

  return animal.age > 10 && animal.type === 'dog';

});