From "Operating Systems: Three Easy Pieces" chapter on "Process API" (section 5.4 "Why? Motivating The API") [1]:
... the separation of fork() and exec() is essential in building a UNIX shell,
because it lets the shell run code after the call to fork() but before the call
to exec(); this code can alter the environment of the about-to-be-run program,
and thus enables a variety of interesting features to be readily built.
...
The separation of fork() and exec() allows the shell to do a whole bunch of
useful things rather easily. For example:
prompt> wc p3.c > newfile.txt
In the example above, the output of the program wc is redirected into the output
file newfile.txt (the greater-than sign is how said redirection is indicated).
The way the shell accomplishes this task is quite simple: when the child is
created, before calling exec(), the shell closes standard output and opens the
file newfile.txt. By doing so, any output from the soon-to-be-running program wc
are sent to the file instead of the screen.