The practical goal is to hide a secret key inside a program, so e.g. implement an algorithm which might involve decryption and signing a message without giving external parties ability to decrypt messages.
The connection between indistinguishable obfuscation formalism and "can't extract secret key" property is not obvious. Here's a quote from a paper which Vitalik linked:
> 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, who showed that (efficiently computable) indistinguishability obfuscators achieve the notion of Best-Possible Obfuscation : Informally, a best-possible obfuscator guarantees that its output hides as much about the input circuit as any circuit of a certain size
In a sense, Vitalik is "recruiting" with this post, his goal being lower the barrier of entry to this discipline.
Is there still such a thing?
Cryptographers have proven that it's possible to use this as a primitive from which you can rebuild the rest of common cryptographic primitives (public encryption, symmetric encryption, etc). So--if it's possible to put this together it'll be a novel construction for every cryptographic primitive that also dodges some of the problems with key distribution and negotiation.
The formalisms of "indistinguishability" in the blog posts are indeed weird.
Some security proofs argue that an attacker cannot distinguish between some plaintext and a string of NUL bytes of the same length being encrypted just by observing ciphertexts. That seems to be what Vitalik is, vaguely, gesturing towards?
(I'm not affiliated with the author or any of their numerous projects, so take my remarks with an appropriate dose of salt.)