Summarizing powers: activate!
The Black Glove is an organization composed of some of the richest and most powerful people in the world, who gather to observe contests orchestrated between good and evil. The guy in charge appears to be Dr. Hurt, who appeared in a Pre-Crisis story which saw Batman, earlier in his career, take part in a military isolation experiment, the effects of which he hoped would give him insight into the Joker's psyche.
At the time, of course, Hurt just appeared to be a run-of-the-mill scientist. Morrison's run has revealed him to be quite the nutbag. During this experiment, for reasons presently unknown, he used this opportunity to really mess with Batman. One of the things he did was attempt to create three replacement Batman, based on what he observed of the real Batman. For example, he determined that tragedy was a defining element of Batman, so he did some pretty awful stuff to these three replacement Batmen. The other thing he did was implant some psychological conditioning in the real Batman. He, of coursed, removed all memory of the incident from batman's mind, so as far as Batman ever knew, the experiment went as intended, and any weird things he experienced were just hallucinations induced as part of said experiment.
In RIP, Dr. Hurt puts in motion a plan to kill Batman, ostensibly for the enjoyment of the Black Glove. He uses a trigger that activates the psychological conditioning implanted years earlier. What this does is effectively turn "off" Batman. He drugs Bruce up and leaves him in the street. As the result of the "turning off,' Bruce has no memory of himself or Batman. As it turns out, though, Batman had planned for the possibility that someone might mount a psychological attack such as this. As he wanders the street, a backup personality activates in his psyche. This is effectively a second personality--a second version of Batman--designed to take over in an event like this. This personality calls itself the Batman of Zur-En-Arrh, and is based on a halucination Batman once suffered that involved an alien Batman (the Batman of Zur-En-Arrh).
This personality isn't quite the same as the regular Batman. Because Bruce Wayne has been "turned off" in his head, this is effectively a version of batman without the balance Bruce Wayne brings to the equation. Furthermore--possibily the result of all the crazy drugs he was loaded up with--Batman is imagining that Bat-Mite is following him around, giving him advice.
Anyways, Batman has now gone to Wayne manor and confronted Dr. Hurt--who has enlisted the aid of the Joker, and Jezebel Jet, who has been a love interest for Bruce recently but now appears to be working with the Black Glove.