What are the PHP operators "?" and ":" called and what do they do?

This is the conditional operator.

$x ? $y : $z

means "if $x is true, then use $y; otherwise use $z".

It also has a short form.

$x ?: $z

means "if $x is true, then use $x; otherwise use $z".

People will tell you that ?: is "the ternary operator". This is wrong. ?: is a ternary operator, which means that it has three operands. People wind up thinking its name is "the ternary operator" because it's often the only ternary operator a given language has.

It's called a ternary operator. If the first expression evaluates to true, HTTPS_SERVER is used, else HTTP_SERVER is chosen.

It's basically a shorthand if statement, and the above code could also be rewritten as follows:

if ($request_type == 'SSL') {
   HTTPS_SERVER;
}
else {
   HTTP_SERVER;
}

This is sometimes known as the ternary conditional operator. Ternary means that it has three arguments, as x ? y : z. Basically, it checks if x is true; if it is, then put y instead of this operation, otherwise z.

$hello = $something ? "Yes, it's true" : "No, it's false";

This is a short way of writing if sentences. It is also used in other languages like Java, JavaScript and others.

Your code,

$protocol = $request_type == 'SSL' ? HTTPS_SERVER : HTTP_SERVER;

can be written like this:

if ($request_type == 'SSL')
    $protocol = HTTPS_SERVER;
else
    $protocol = HTTP_SERVER;

That is a one line if statement:

condition ? true : false

Translated to an ordinary if statement in your case, that would be:

if($request_type == 'SSL') HTTPS_SERVER;
else HTTP_SERVER;

That's basically a fancy way of writing an if-else statement. Some say it's easier to read, some say not.

Ternary operator at Wikipedia

This works like an if statement it's very simple and easy once you get used to it. (conditions_expressions) ? what_to_do_if_true : what_to_do_if_false.

As John T says, it is called a ternary operator and is essentially a shorthand version of an if /else statement. Your example, as a full if / else statement, would read;

if($request_type == 'SSL')
{
    HTTPS_SERVER;
}
else
{
    HTTP_SERVER;
}