Calling Functions - GNU Emacs Lisp Reference Manual

Defining functions is only half the battle. Functions don't do anything until you call them, i.e., tell them to run. Calling a function is also known as invocation.

The most common way of invoking a function is by evaluating a list. For example, evaluating the list (concat "a" "b") calls the function concat with arguments "a" and "b". See Evaluation, for a description of evaluation.

When you write a list as an expression in your program, you specify which function to call, and how many arguments to give it, in the text of the program. Usually that's just what you want. Occasionally you need to compute at run time which function to call. To do that, use the function funcall. When you also need to determine at run time how many arguments to pass, use apply.

— Function: funcall function &rest arguments

funcall calls function with arguments, and returns whatever function returns.
Since funcall is a function, all of its arguments, including function, are evaluated before funcall is called. This means that you can use any expression to obtain the function to be called. It also means that funcall does not see the expressions you write for the arguments, only their values. These values are not evaluated a second time in the act of calling function; the operation of funcall is like the normal procedure for calling a function, once its arguments have already been evaluated.
The argument function must be either a Lisp function or a primitive function. Special forms and macros are not allowed, because they make sense only when given the “unevaluated” argument expressions. funcall cannot provide these because, as we saw above, it never knows them in the first place.
          (setq f 'list)
               => list
          (funcall f 'x 'y 'z)
               => (x y z)
          (funcall f 'x 'y '(z))
               => (x y (z))
          (funcall 'and t nil)
          error--> Invalid function: #<subr and>
     
Compare these examples with the examples of apply.

— Function: apply function &rest arguments

apply calls function with arguments, just like funcall but with one difference: the last of arguments is a list of objects, which are passed to function as separate arguments, rather than a single list. We say that apply spreads this list so that each individual element becomes an argument.
apply returns the result of calling function. As with funcall, function must either be a Lisp function or a primitive function; special forms and macros do not make sense in apply.
          (setq f 'list)
               => list
          (apply f 'x 'y 'z)
          error--> Wrong type argument: listp, z
          (apply '+ 1 2 '(3 4))
               => 10
          (apply '+ '(1 2 3 4))
               => 10
          
          (apply 'append '((a b c) nil (x y z) nil))
               => (a b c x y z)
     
For an interesting example of using apply, see Definition of mapcar.

It is common for Lisp functions to accept functions as arguments or find them in data structures (especially in hook variables and property lists) and call them using funcall or apply. Functions that accept function arguments are often called functionals.

Sometimes, when you call a functional, it is useful to supply a no-op function as the argument. Here are two different kinds of no-op function:

12.5 Calling Functions