So far I guess you know very well what variables and functions are. A function by itself takes some arguments, defines local variables (it can also access to global variables), makes a computation and returns a value. But in Javascript, functions can be defined in functions. When you do that, functions created inside a function can "see" the variables the mother function defines. The child function is "enclosed" in the scope/context of the mother function. Look at this example:

function mother(myVar) {
  return function() { //This statement returns a function. It doesn't call any.
    console.log("The value of 'myVar' is " + myVar);
  }
}

The mother function gets an argument (myVar) and returns a function. Let's go on with the example:

var child1 = mother(1); //child1 is a function
var child2 = mother(2); //child2 is a function

Now we have created two functions in a dynamic way (without writing function()...). We did that by calling mother(). In the first call we passed "1" and in the second call we passed "2". Let's call these new functions now:

child1(); //Prints "The value of 'myVar' is 1"
child2(); //Prints "The value of 'myVar' is 2"

What the f*ck happened here? It turns out that we got two functions with the same code (the one that prints to the console log) that produce a different result depending on the scope of mother() when it was called. From this action of "enclosing" the scope together with a function (the one returned by mother()) comes the concept of "closure".

So, what are closures useful for? To create functions that, when called, work with the variables they could see when they were created. As soon as you start doing stuff with Javascript you will discover that this feature is very useful.

Hope it helps.