In Lisp, closures are an important feature that allows functions to retain references to their surrounding lexical environment, including the values of variables, even after the outer function has finished executing. A closure is created when a nested function references variables from its containing scope, effectively "closing over" those variables. Here are the key aspects of closures in Lisp:

1. Lexical Scoping : Lisp uses lexical scoping, which means that the scope of a variable is determined by its position in the source code. When a function is defined, it captures the variables in its lexical environment.

2. Nested Functions : Lisp allows functions to be defined within other functions. These nested functions have access to the variables defined in their containing function.

3. Capture of Variables : When a nested function references a variable from its containing scope, a closure is created. The closure includes both the function and the environment in which it was defined. This captured environment is stored as part of the closure, enabling the function to access the variables even after the containing function has finished executing.

4. Deferred Execution : Closures allow for deferred execution of code. The enclosed function can be passed around, stored in data structures, or returned as a result. Later, when the enclosed function is called, it maintains access to the captured variables, allowing it to operate on them.

5. Data Privacy and Encapsulation : Closures provide a way to achieve data privacy and encapsulation by controlling access to variables. The variables captured in the closure are accessible only within the enclosed function, protecting them from being modified or accessed from outside the closure.

Closures in Lisp are particularly powerful because they allow for the creation of functions with persistent state and behavior tied to the captured environment. They enable functional programming techniques such as currying, partial application, and the creation of higher-order functions. Here's an example that demonstrates the concept of closures in Lisp :

(defun make-counter ()
  (let ((count 0))
    (lambda ()
      (setq count (1+ count))
      count)))

(setq counter (make-counter))
(funcall counter) ; Returns 1
(funcall counter) ; Returns 2​

In this example, the function `make-counter` returns a closure that captures the variable `count` from its containing scope. The returned closure is assigned to the variable `counter`. Each time the closure is called with `(funcall counter)`, it increments the `count` variable and returns its updated value. The `count` variable is preserved within the closure, maintaining its state across multiple function calls.

Closures provide a powerful mechanism for creating flexible and reusable code in Lisp, facilitating the implementation of advanced programming patterns and techniques.