What does autoload do in zsh?

autoload tells zsh to look for a file in $FPATH/$fpath containing a function definition, instead of a file in $PATH/$path containing an executable script or binary.

Script

A script is just a sequence of commands that get executed when the script is run. For example, suppose you have a file called hello like this:

echo "Setting 'greeting'"
greeting='Hello'

If the file is executable and located in one of the directories in your $PATH, then you can run it as a script by just typing its name. But scripts get their own copy of the shell process, so anything they do can't affect the calling shell environment. The assignment to greeting above will be in effect only within the script; once the script exits, it won't have had any impact on your interactive shell session:

$ hello
Setting 'greeting'
$ echo $greeting

$ 

Function

A function is instead defined once and stays in the shell's memory; when you call it, it executes inside the current shell, and can therefore have side effects:

hello() {
  echo "Setting 'greeting'"
  greeting='Hello'
}

$ hello
Setting 'greeting'
$ echo $greeting
Hello

So you use functions when you want to modify your shell environment. The Zsh Line Editor (ZLE) also uses functions - when you bind a key to some action, that action is defined as a shell function (which has to be added to ZLE with the zle -N command).

Now, if you have a lot of functions, then you might not want to define all of them in your .zshrc every time you start a new shell; that slows down shell startup and uses memory to store functions that you might not wind up calling during the lifetime of that shell. So you can instead put the function definitions into their own files, named after the functions they define, and put the files into directories in your $FPATH, which works like $PATH.
Zsh comes with a bunch of standard functions in the default $FPATH already. But it won't know to look for a command there unless you've first told it that the command is a function.

That's what autoload does: it says "Hey, Zsh, this command name here is a function, so when I try to run it, go look for its definition in my FPATH, instead of looking for an executable in my PATH."

The first time you run command which Zsh determines is autoloaded function, the shell sources the definition file. Then, if there's nothing in the file except the function definition, or if the shell option KSH_AUTOLOAD is set, it proceeds to call the function with the arguments you supplied. But if that option is not set and the file contains any code outside the function definition (like initialization of variables used by the function), the function is not called automatically. In that case it's up to you to call the function inside the file after defining it so that first invocation will work.

The autoload feature is not available in bash, but it is in ksh (korn shell) and zsh. On zsh see man zshbuiltins.

Functions are called in the same way as any other command. There can be a name conflict between a program and a function. What autoload does is to mark that name as being a function rather than an external program. The function has to be in a file on its own, with the filename the same as the function name.

autoload -Uz vcs_info

The -U means mark the function vcs_info for autoloading and suppress alias expansion. The -z means use zsh (rather than ksh) style. See also the functions command.

Edit (from comment, as suggested by @ijoseph):

So it records the fact that the name is a function and not an external program - it does not call it unless the -X option is used, it just affects the search path when it is called. If the function name does not collide with the name of a program then it is not required. Prefix your functions with something like f_ and you will probably never need it.

For more detail see http://zsh.sourceforge.net/Doc/Release/Functions.html.