Nearly everyone has played this one. If you yourself are too young to have played it, I can almost 100% promise that your parents have. Originally made in 1985 and world popularised in 1989 by being released with the "new at the time" Original Gameboy, Tetris was THE addictive puzzler in computer gaming and by god was it.
The premise is fairly simply, as should be with all puzzle games that want to welcome in anyone and keep them a long time playing the game. You have a blank area that's about 9 blocks wide and about 30 blocks high (depending upon versions, some go to STUPID lengths of having thousands of blocks wide). Within this area, Tetriminoes (Check the official company for the spelling, they don't like "Tetrominoes"), descend from the top of the area and fall steadily towards the bottom. These are shapes made up of arrangements of 4 blocks to form 7 unique shapes. Once they hit the bottom, they stick and become immobile, where upon a new shape will fall from the top again.
The game is about making entire full rows of blocks line up by fitting, slotting and shifting the shapes into an appropriate position so that a whole, horizontal line can be completed from one side to another. Once this is achieved, that line disappears and everything above that line drops down to fill the now-empty space. Giving the player more space to keep playing. The score goes up depending upon the number of lines cleared (a maximum of 4 lines from using a 4x1 shaped piece) and while the score goes up, the speed of the game goes up too.
Different game modes allow for playing either to get to 200 lines and by extension, level 20 in speed which leaves you virtually NO time to shift falling blocks into place or rotate them. Or the other mode where you have to beat the game by getting 25 lines but starting with arenas that have randomly filled walls-with-gaps already in place. Other variations of the game include things like having special blocks within the shapes that act as bombs, or using the ability to store a piece for later use, or getting specific back-to-back combinations of line removals for further bonuses. Or even a vs. mode where getting rid of sets of lines will bump up your opponents lines but in such a way that they could quickly reverse the lines being sent to them and send them back with interest.
Other games and variations have Wordtris where the blocks are made up of scrabble shapes and you have to make words rather than making lines, or you have the ill-conceived Sextris where you're dropping in naked people in various positions and have to remove them by getting them into hump-able positions (I had a very odd childhood didn't I...) before they vanish and allow for more naked people to fall into the fray. Or it could be that you're playing the game in 3D and have multiple layers in the Z-Axis to fill too, or you're playing it in First Person Mode or it's about using shapes to create platforms for a platform jumping character (Mario usually...) to progress across the level in some fashion or another.
Later iterations of the game would play online and allow people to compete around the world in 8way games and having team modes and such. Basically as the technology increases and new elements of gaming are found, someone somewhere is going to add in a Tetris effect along the lines from porn to faces, hats, 3D shapes, rotating the arena rather than the pieces, gravity/physics effects and so on.
The base game however, is still just dropping blocks into an area and filling up a space neatly. It appeals on a LOT of levels and in particular, the OCD group, as this is the ultimate cleaning up game.
It's because the game is so simple and accessible that virtually everyone and their parents have played this at one time or another in some fashion or another. Even adventure games have variations of sorting and arranging spaces, such as Resident Evil 4 where in the inventory, you had to make sure everything was neatly packed away or you'd have difficulties buying new items and such. A bit of a weak example, I know, but the influence is still there and can be found in a great many other games through the ages, even parody examples in games like I Wanna Be The Guy (Press R now, just do it)
As such it's hard to just review Tetris given that it's the phenomenon that it has become, but perhaps that should be the focus rather than the game itself. This is a game that started as a puzzle game and ended up transcending time space and the 4th dimension in some versions of the game where a 2D plane has 4D shapes represented by 3D displays in the 2D plane and changes through versions of itself bending inside and outside to form tesseracts (Hyper cubes) and then fitting THOSE into the area to clear out lines.
How the hell someone is going to get their head around that one ... Actually it's quite a fun game once your mind starts to see things in 4 dimensions.
But this just shows how adaptable a player can become from such humble beginnings within a game. There's no save function it's just you and the area. While there have been a GREAT many contenders to the throne, from columns to bean games, to puzzle fighter and so on, Tetris remains such a firm staple of video game history that very rarely can a falling block puzzle game be made that doesn't owe something to Tetris. It's quick, easily playable (especially the original versions, new versions sometimes over complicate things) and of such a pick-up-and-play focus that you can sit down for a session or two and be done within 5 minutes or find that you're looking outside and the 4 Horsemen are looking over your shoulder and waiting for you to catch up with the rest of the apocalypse because you were too busy to join the rapture.
And I bet they'll want to play it before claiming your sorry soul, and they'll likely be better at than you.