If you're at all interested in preserving your history on the site, you'll want to download your data either directly from posts or through Yahoo's Privacy Dashboard.
Yahoo hasn't formally explained the shutdown, but you could see this coming. Yahoo launched Groups in 2001 as a sort of forum and mailing list hybrid, and it quickly became a home for specialist communities. There was one major problem, however: social networking happened. There's not as much incentive to use Yahoo's community when your Facebook group, Twitter friends or Discord chat will fit the bill, and often more effectively.
Still, this could be a sad moment for some. Much like the GeoCities shutdown, Yahoo is erasing a piece of internet history. Even if you haven't used Yahoo Groups in years, you might still have a presence there -- say, a fan club for a favorite band from your youth. Yahoo is effectively erasing that historical record, even if it's likely to live on through archive services.
Update 10/17 3:52PM ET: Yahoo has moved the shutdown date from the originally listed 21st to the 28th. We've updated the story accordingly.