Explain the concept of closures in functional programming.

Closures in functional programming are functions that have access to variables from their outer scope.

In more detail, a closure is a function bundled with its lexical environment. Lexical environment means the environment in which the function was declared. This environment consists of any local variables that were in-scope at the time the closure was created. Closures allow a function to access variables from an outer function that has already returned, even though its scope is 'closed' over the local variables it defines. This is why they are called 'closures', as they 'close over' the variables they need.

In functional programming, closures are used to encapsulate private variables, similar to how objects are used in object-oriented programming. They can also be used to create function factories, where a function generates and returns another function with specific characteristics.

Let's consider an example to illustrate this concept. Suppose we have a function 'outer' that defines a variable 'x' and a function 'inner'. The 'inner' function is a closure that has access to 'x'. Even after the 'outer' function has finished executing, the 'inner' function still has access to 'x'. This is because 'inner' is a closure that 'closes over' the variable 'x'.

```javascript
function outer() {
let x = 10;
function inner() {
console.log(x);
}
return inner;
}

let myFunction = outer();
myFunction(); // This will log '10' to the console
```

In this example, 'myFunction' is a closure that has access to the variable 'x' from its outer scope. Even though the 'outer' function has finished executing, 'myFunction' can still access 'x'. This is a powerful feature of functional programming that allows for data privacy and function factories.

In conclusion, closures are a fundamental concept in functional programming that allow functions to have 'private' variables that persist even after the function has returned. They are a powerful tool for encapsulating data and creating complex function structures.