$_REQUEST is a super global array. Just like $_GET, $_POST, $_COOKIE, $_SESSION etc. That means it can store a list information numerically or associatively.
For example:
Associative:
$array = array(key->value, key->value);
Numeric:
$array = array([0]->value, [1]->value);
In the case of $_REQUEST or $_POST or $_GET these arrays will store encoded data sent to the PHP header.
for example:
$_REQUEST['key'] = value;
or
you have a navigation item:
<a href='?key=value'>value</a> //for $_GET
PHP will encode that key->value into the url and save it to the super global array that you are using. To access it call:
echo $_REQUEST['key']; //returns 'value'
In your case msg is, so far, not encoded to the browser. It needs to be passed by different means(forms, href's etc.). So,
$_REQUEST['msg'] = 'new';
if(isset($_REQUEST['msg']{ \\use isset() to avoid an error
if($_REQUEST['msg'] == "new"){
$message = "New User has been added successfully";
}else if($_REQUEST['msg'] == 'edit'){
$message = "User has been saved successfully";
}else if($_REQUEST['msg'] == 'update'){
$message = "User(s) has been Updated successfully";
}
} //returns $message = "New user..."
$_REQUEST is not suggested because it makes it hard to control what information is processed. $_GET requests show the key->value pairs in the url. Information that you don't want as visible probably shouldn't be shown there. With $_REQUEST a user can send that key->value pair over the url to see what information needs to be passed and exploit that in other ways (google cross-site request forgeries).
TL;DR : $_REQUEST['msg'] -- 'msg' is a key in a key->value pair ('new'| 'edit' | 'update' being the value)
$_REQUEST is a superglobal array that saves values that can be used by the user in any scope in other parts of the website.