Well it's basically a puzzle game (very successful and popular one especially in Japan) made by SEGA/Sonic Team, not to bore you with details of how the series came to be and why it's often associated with "Dr Robotnik" in the west (or in some rare cases Kirby) but it's another Tetris-like puzzler that's quite addictive, I'd recommend Puyo Puyo 15th Anniversary if you're interested in checking it out, it's also available on the DS as well as PSP (among other consoles) so if you have a modded PSP or a flash card for the DS you can try it out, they released Puyo Puyo Tetris not long ago on the PS4 and Switch outside of Japan (while in Japan that game came out in 2014), making it the first localized Puyo Puyo game since 2003, it's received highly positive reviews.
Oh, and the term "Puyo Puyo" is Japanese for "squishy-squishy" often used to describe boobies and such, but it has nothing to do with boobies in this game, although there were some hentai officially released Puyo Puyo games back when the series was owned by Compile, now known as Compile Heart which are known with the Hyperdimension Neptunia games.
Well it's basically a puzzle game (very successful and popular one especially in Japan) made by SEGA
