It's got a lot to do with the phrase first used by Shakespeare- "Vanished into air". He used that phrase to depict something that suddenly disappeared into, well, nothing. Therefore, the phrase "out of thin air' alludes to something that has appeared out of nothing, suddenly. As for 'thin' - who knows?!

So in this quote it is saying that confidence in yourself seems to come out of nothing/nowhere. Hope that helps!

As Alex says, 'thin air' is an idiomatic expression meaning 'nowhere'.

A common expression we use when something or someone suddenly disappears is 'they vanished into thin air'.