The most voted answer is wrong or at least not completely true as the OP is talking about blank strings only. Here's a thorough explanation:

What does empty mean?

First of all, we must agree on what empty means. Do you mean to filter out:

1. the empty strings only ("")?
2. the strictly false values? ($element === false)
3. the falsey values? (i.e. 0, 0.0, "", "0", NULL, array()...)
4. the equivalent of PHP's empty() function?

How do you filter out the values

To filter out empty strings only:

$filtered = array_diff($originalArray, array(""));

To only filter out strictly false values, you must use a callback function:

$filtered = array_diff($originalArray, 'myCallback');
function myCallback($var) {
    return $var === false;
}

The callback is also useful for any combination in which you want to filter out the "falsey" values, except some. (For example, filter every null and false, etc, leaving only 0):

$filtered = array_filter($originalArray, 'myCallback');
function myCallback($var) {
    return ($var === 0 || $var === '0');
}

Third and fourth case are (for our purposes at last) equivalent, and for that all you have to use is the default:

$filtered = array_filter($originalArray);