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.