What are higher order functions in functional programming? How does the 'map' function work and why is it a higher order function?

Higher order functions either have one or more arguments that are themselves functions, return a function as their result, or both. Arguments to higher order functions can themselves be higher order functions, though this is not a requirement. 
The ‘map’ function requires both a function and a list be passed as arguments. Since it requires a function as argument, 'map' must be a higher order function. The function that is passed as an argument is applied to every element of the list (using each element as the argument of the passed function), to form a new list of results. The resulting list will have the same length but may have a different type to the initial list, depending on the function used as argument.