I think you're referring to what are commonly called air quotes.
The gesture can mean different things but mostly it's to reinforce the sarcasm/scepticism/irony that you want to express. It often equates to the phrase "so-called".
a) I saw her having lunch again with that guy she says is her <<work colleague>>. (<< = air quotes)
b) He's not just a work colleague, they've been dating for weeks.
a) That's what I thought!
not a teacher