I quote wikipedia:

In mathematics and computer science, a higher-order function (also functional, functional form or functor) is a function that does at least one of the following: takes one or more functions as arguments (i.e., procedural parameters), returns a function as its result.

• function(callback) { /do something else/ return callback;}
• function(param) { var f = function() { return 1;} return f; };
• function (callback) { / do something / callback(); }

those would be higher order function. :)

sort(), map() and reduce() are all examples of higher order functions. They all take a function or lambda as a parameter

const a = [3,7,1,2,4,8];
const b = a.sort((f, n) => f < n);
console.log(b);
> [ 8, 7, 4, 3, 2, 1 ]

This video will explain you it very well Higher-order functions - Part 1 of Functional Programming in JavaScript

I have difficulties describing it, but here's an example from what I know (and might be totally wrong):

function greet(name, salutation) { return 'Hello ' + salutation + ' ' + name }
greet('Foo', 'Mr') // => 'Hello Mr Foo'

// higher order function
function greetMr (name) { return greet(name, 'Mr') }
greetMr('Foo') // => 'Hello Mr Foo'

Here greetMr is an example of a higher order function, CMIIW