In Lisp, higher-order functions are functions that can take other functions as arguments and/or return functions as results. The concept of higher-order functions is a fundamental aspect of functional programming and is fully supported in Lisp. Here's an explanation of the concept and the benefits it offers:

1. Functions as Arguments :
   * In Lisp, functions are first-class objects, which means they can be treated like any other data type.
   * Higher-order functions in Lisp can accept other functions as arguments. These functions can be passed as arguments to higher-order functions just like any other data value.
   * This ability to pass functions as arguments enables the creation of more flexible and reusable code. It allows functions to be customized and extended by providing different behavior through function arguments.

2. Functions as Return Values :
   * Higher-order functions in Lisp can also return functions as results.
   * This means that a function can generate and return a new function based on its arguments or the computation it performs.
   * Returning functions as results allows for the creation of specialized or customized functions on the fly, providing a way to generate code dynamically.
   * This ability to return functions as results enables the creation of abstractions and control structures that would be challenging to express using only fixed functions.

3. Function Composition :
   * Higher-order functions allow for function composition, where multiple functions can be combined to form a new function.
   * Function composition involves taking the output of one function and using it as the input for another function, creating a chain of function calls.
   * The `compose` function, for example, is a higher-order function that takes two functions as arguments and returns a new function representing their composition.
   * Function composition allows for the creation of complex behavior by combining simpler functions, promoting modularity, and code reuse.

4. Callback Functions :
   * Higher-order functions are particularly useful for implementing callback mechanisms.
   * A callback function is a function that is passed as an argument to another function and gets invoked at a specific point during the execution of that function.
   * Callback functions allow for event-driven programming and handling of asynchronous operations, making Lisp programs more responsive and flexible.