There are three main contributions of the research
A proposed indistinguishability obfuscation for NC1 circuits where the security is based on the so called Multilinear Jigsaw Puzzles (a simplified variant of multilinear maps).
Pair the contribution in 1 with Fully Homomorphic Encryption and you get indistinguishability obfuscation for all circuits.
Combine 2 with public key encryption and non-interactive zero-knowledge proofs and you functional encryption for all circuits. I believe that prior to this functional encryption for all circuits was not possible.
So, lets look at these in turn.
Indistinguishability obfuscation (contributions 1 and 2)
From the paper
It is important to note that unlike simulation-based definitions of obfuscation, it is not immediately
clear how useful indistinguishability obfuscators would be. Perhaps the strongest philosophical justification
for indistinguishability obfuscators comes from the work of Goldwasser and Rothblum [GR07], who showed
that (efficiently computable) indistinguishability obfuscators achieve the notion of Best-Possible Obfuscation [GR07]: Informally, a best-possible obfuscator guarantees that its output hides as much about the input circuit as any circuit of a certain size.
Thus, the main contributions when it comes to Indistinguishability obfuscation of this paper is to show a construction for IO that works on all circuits, then pair that with a few other things to get functional encryption for any circuits.
Note that the usefulness of IOs will only become greater as time goes one. As seen in another paper by some of the same authors and hopefully they will become more practical as new constructions are proposed.
Functional Encryption (contribution 3)
Prior to this work FE has only been possible on small circuits. Using 1 and 2, with some other crypto primitives, the authors were able to build FE on all circuits. That is a very significant result.
What does this mean for Anti-RE
It would appear that by itself, indistinguishability obfuscation means very little for anti-reverse engineering. FE on any circuit, however, could be significant. Here is the reason. FE allows for results of a computation to be in plaintext. Compare this with fully homomorphic encryption (FHE) where results will be encrypted or with Multiparty Comptuation were we require multiple parties (but can have plaintext results). Thus, I could give you a key which would allow you to, say, AES decrypt any data I send to you. You would never know the AES key though. There are techniques that also allow you to hide the function (not just the inputs).
Imagine if you had the ability to allow someone to compute only a specific function(s) on private data that I send you and still get plaintext results. Furthermore, the function is hidden, so they can't reverse engineer the function. That is the contribution of FE, and FE on any circuit is what this work enables.
From what I see in the paper, contribution 1 could be practical for real world use, though I am not completely sure. Multilinear maps are pretty inefficient at the moment, but the construction used here is somewhat simplified. Since 2 uses FHE, it isn't practical yet. Since 3 uses 2 and some other heavy-weight crypto, it is also, not practical at the time.