Welcome to Elixir @Earl

This is returning the capture IO.puts. The parameter message is unused in the above code.

You might have got a warning when the code was compiled.

warning: variable "message" is unused (if the variable is not meant to be used, prefix it with an underscore)
  iex:10: ModuleName.talk/1

We can remove the unused variable message from the code.
If you want to print Hello World, you will have to do something like this -

defmodule ModuleName do
  def talk(), do: &IO.puts/1
end
# then in iex  
iex> ModuleName.talk().("Hello World") 
Hello World
:ok

One other thing is IO.puts returns :ok - it writes “Hello World” to standard output.

Edit: added info about IO.puts return

One thing I’ve found really really important for folks learning a language: be very specific about the difference between “returning a value” and “printing a value”. Starting out in a REPL like iex can obscure this distinction, and it’s important to build a correct mental model.

IO.puts("Hello world") does two things:

• it prints the string Hello world!
• it returns the atom :ok

def talk(message), do: &IO.puts/1
msg = ModuleName.talk("Hello World!")

What is going on there is that you are returning &IO.put/1 but this anonymous function knows nothing about message

you should do something like this

def talk(message), do: fn -> IO.puts(message) end
msg = ModuleName.talk("Hello World!")

#and then apply msg (anonymous function of arity-0
msg.()