<?php

$emailstring = "John Bo <jboe@gmail.com>,<other@email.com>, abracadbra@gmail.com, <asking@gmail.com>";
$emails = explode(',',$emailstring);

for ($i = 0; $i < count($emails); $i++) {
    if (strpos($emails[$i], '<') !== false) {
        $emails[$i] = substr($emails[$i], strpos($emails[$i], '<')+1);
        $emails[$i] = str_replace('>','',$emails[$i]);
    }
    $emails[$i] = trim($emails[$i]);
}

print_r($emails);

?>

Array
(
    [0] => jboe@gmail.com
    [1] => other@email.com
    [2] => abracadbra@gmail.com
    [3] => asking@gmail.com
)