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Both authors are giants of dualities and equivalences so the main idea of the paper may be expressed as a new kind of duality – the existence of two seemingly different but ultimately exactly equivalent descriptions – which may be expressed by their formula
This equation says that the Einstein-Podolsky-Rosen entanglement is the same thing as the Einstein-Rosen bridge. You may be tempted to cancel ER and disrespectfully deduce that Podolsky is equal to zero. However, you shouldn't forget that the equation above is one of a multiplicative rather than additive sort so the right conclusion is that Podolsky is the number one. ;-)
The new paper starts with some comments you have seen on TRF many times: EPR-style entanglement doesn't represent any genuine non-locality. It doesn't allow you to send any genuine information to spacelike-separated regions of the spacetime i.e. faster than light. Correlation isn't causation; quantum mechanics predicts correlation for EPR-style experiments but the correlation/entanglement is a consequence of the objects' mutual contact in the past when the state of the whole system was prepared, not a consequence of any action at a distance in the moment of the measurement.
There is another concept that doesn't allow you to send the information superluminally although you could naively think that it can: the Einstein-Rosen bridge. This is a technical name for a special wormhole, one that is constructed by gluing and/or maximally extending the vacuum solutions of Einstein's equations of general relativity i.e. things similar to Schwarzschild's solution for an empty and neutral black hole.
A reason why this sort of a "non-traversable" wormhole doesn't allow any standard faster-than-light communication (at least not a permanent one) is simply the black-hole-like appearance of the exterior of the wormhole (on both sides): you may only catch the would-be information that has propagated through the wormhole if you actually jump into the black hole but in that case, you de facto commit suicide and give up the right to exchange the information forever. Once you jump to the black hole, you may say that your position with respect to the exterior asymptotic region of the spacetime is "confusing". You are somewhere in between the original two widely separated places, not in the vicinity of either of them, so your perceptions shouldn't affect the question whether the two separated places may exchange the information. They cannot and you don't belong to those places anymore!
So both ER and EPR are concepts that could naively allow you to send the information faster than light; but both of them actually refuse to do so. They share these two properties so they could be the same thing. Of course, it's not a proof that they're the same thing which is why Maldacena's and Susskind's claim that they are actually the same thing both non-obvious and non-vacuous contribution to physics if it is true. And they have some more detailed evidence that it actually is true.
Whenever there are two objects that are entangled, one may view this entanglement as the existence of a wormhole of some kind. However, in most cases, such a wormhole is Planckian, so to say, and it requires the full theory of quantum gravity – going well beyond the effective long-distance theory similar to general relativity – to be properly studied. (I can't resist to think about the thin handles that may be added to M2-branes modeled by Matrix theory without changing the state described by the noncommutative geometry; their spacetime wormholes must be analogous to these "world volume wormholes".) They admit so: they reinterpretation of the entanglement as an Einstein-Rosen wormhole may often be just an academic formality that doesn't allow you to exploit the useful properties we like to associate with large and thick wormholes.
On the other hand, they accumulate quite some evidence that a greater number of examples of entanglement than what you might think may be described in terms of the Einstein-Rosen wormhole that is really large and classical and unquestionably deserves the title.
In particular, they suggest that once a black hole evaporates one-half of the original entropy, i.e. after the Page time when we know the early radiation to be almost maximally entangled with the remaining black hole, one automatically gets the "thermofield-like" doubling of the degrees of freedom – doubling of the number of black holes. The early Hawking radiation may be interpreted as one of the two black holes that is connected (after some transformation of its degrees of freedom) to the remaining, self-evident black hole by the Einstein-Rosen bridge.
The authors claim that this has consequences for the perceptions felt by an observer who jumps into the remaining black hole: his perceptions – which may include the firewall-like death near the horizon – are actually affected by the decision what some other observers do with the early Hawking radiation! After all, manipulating with the early Hawking radiation should be interpreted as processes "somewhere inside the wormhole" so these processes may be thought of as appearing "geometrically close to the black hole interior" because this is where the second exit from the wormhole resides!
Whether or not such an influence of the "experimenter measuring the early Hawking radiation" on the "infalling observer" violates any notion of locality and how strongly is a subtle question that requires you to be careful. Clearly, some locality as defined strictly by classical general relativity (and assuming the non-wormhole relationships between events in spacetime!) has to be violated because the measurements of the early Hawking radiation can't be connected by any time-like trajectory with the events in the remaining black hole interior. However, they are connected in more general ways.
Even if the infalling observer is able to miraculously find out something about the activities done by very distant, seemingly spacelike-separated experimenters who measure the early Hawking radiation, it doesn't imply any real paradox that we may derive from faster-than-light communication simply because the infalling observer has no way of communicating his perceptions to the folks outside the nearby event horizon.
We shouldn't overstate the reasons why we believe principles such as locality. We believe them because in combination with the Lorentz invariance, faster-than-light communication would be equivalent to the changes of the past and closed time-like curves that would lead to contradictions. However, if we consider more general situations with "doomed infalling observers" whose doomed fate allows us to avoid the paradoxes, the original evidence in favor of the strict locality really evaporates.
The observer on one side of the Einstein-Rosen bridge may control the perceptions of the other if she acts quickly enough; a section of the paper is dedicated to the question what this condition means. It seems that they want to apply these considerations to the experimenter who manipulates with the early Hawking radiation, too. She has some power over the poor observer who falls into the remaining black hole after the Page time.