Incidentally, many people regard this as very bad usage. Properly, the word "quote" should be used to indicate that you are quoting somebody's exact words, especially if the quote is remarkable or contentious in some way:
The minister then said that his constituents were, quote: The stupidest cretins ever to walk this earth.
You might use the word "unquote" to mark the end of a quote if this is not otherwise obvious:
Professor Nutcase said that the planet Mars, quote, consists of a chocolate crust with a mantle of caramel and a core of nougat, unquote, but most other scientists disagree.
It is true that in writing, instead of writing "quote" and "unquote", we write quotation marks, but in speech we often have to "spell out" the punctuation like this (in this case to make it clear that Professor Nutcase did not say: "Most other scientists disagree").
This has led many people to use the phrase "quote unquote" to signify that something is in quotation marks for any reason at all -- and to say "quote unquote" together at the beginning of the phrase. Purists find this very annoying, and regard this as a lazy way of saying "so-called".
As for "drawing" quotation marks in the air, many people also find that incredibly annoying.
Incidentally, there is a radio panel game, in which panel members have to guess the origins of literary quotations, which is called
Quote ... Unquote. It's off the air at the moment, but you'll find its official homepage
by following this link.