It's a formalism use to analyze security properties, it's not how it is used in practice.

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