It evaluates to the left operand if the left operand is truthy, and the right operand otherwise.

In pseudocode,

foo = bar ?: baz;

roughly resolves to

foo = bar ? bar : baz;

or

if (bar) {
    foo = bar;
} else {
    foo = baz;
}

with the difference that bar will only be evaluated once.

You can also use this to do a "self-check" of foo as demonstrated in the code example you posted:

foo = foo ?: bar;

This will assign bar to foo if foo is null or falsey, else it will leave foo unchanged.

Some more examples:

<?php
    var_dump(5 ?: 0); // 5
    var_dump(false ?: 0); // 0
    var_dump(null ?: 'foo'); // 'foo'
    var_dump(true ?: 123); // true
    var_dump('rock' ?: 'roll'); // 'rock'
    var_dump('' ?: 'roll'); //  'roll'
    var_dump('0' ?: 'roll'); //  'roll'
    var_dump('42' ?: 'roll'); //  '42'
?>

By the way, it's called the Elvis operator.

Many popular mainstream languages that focus at least somewhat on conciseness have a similar operator, so I'd say that it is fairly common.

First, some notes:

1. For the purposes of this answer, it doesn't matter whether the syntax is ?:, ??, || or or, especially since all are equally concise.
2. What is a "true value" for this operator differs from language to language, and may not be the same as what is considered a "true value" in other contexts (like in an if condition).

Now, let's go though some languages and see what we find:

• C and C++: no Elvis in the standards, since concise syntax sugar does not seem to be focus for these languages
• Java: Elvis was explicitly rejected, seemingly also because syntax sugar is not a focus for Java.
• C#: ?? is a null-checking Elvis
• Python: or works as truthy-checking Elvis
• JavaScript: || works as an Elvis operator that checks for truthiness, ?? is an Elvis operator that only checks for null and undefined
• PHP: ?: is a truthy-checking Elvis, ?? is a null-checking Elvis
• Ruby: || works as a truthy-checking Elvis
• Go: no Elvis, since Go prefers simplicity of language to conciseness of code
• Swift: ?? is a nil-checking Elvis
• Rust: no Elvis, presumably because Rust does not have concepts similar to truthiness or null