If you were leasing one of the offending cars as of September 18, 2015 (when Volkswagen admitted to the emissions rigging), you might be eligible to make a claim, too.
The buyback option
In addition to the cash payouts, people who bought one of the cars prior to September 18, 2015 can opt for Volkswagen to buy the cars back at pre-scandal trade-in values -- from $12,475 for a 2009 VW Jetta to $44,176 for a 2015 Audi A3 TDI Prestige, according to the Bloomberg report. So if you own the aforementioned Jetta and take both the cash compensation and the buyback option, there's a chance you'll get at least $17,575. You just have to decide by May of 2018.
The buyback option, though, is not mandatory. Instead, you can wait for Volkswagen to come up with a fix for the emissions issue that satisfies environmental requirements (it has yet to do so and a fix could reduce engine performance) or you can keep driving your car as it is and simply not participate in the settlement at all. You just won't get any cash with the latter option and will have to live with yourself for further polluting the environment.