From Hard Drop - Tetris Wiki
Garbage is a form of "attack" in multiplayer Tetris that has been around since the days of the Game Boy. The basic gist of it is that if you clear multiple rows of tetrominoes at one time, extra rows, with a gap will add to the bottom of your opponent's playfield.
 Garbage System
The garbage system is simple. The more rows you clear at once, the more garbage rows are sent to your opponent.
|Clear Type||Rows Cleared||Garbage Rows Sent|
|All Clear||1, 2, 3, 4||+7|
|1 Combo||1, 2, 3, 4||0|
|2 or 3 Combos||1, 2, 3, 4||+1|
|4 or 5 Combos||1, 2, 3, 4||+2 (then another +1 for each additional two Combos)|
 Gameplay Example
The left diagram shows the player's field while the right shows his opponent.
If a player "drops" a T here:
It will clear two lines at once, sending one row of garbage to the opponent:
Then, if the player drops a tetris here:
It will clear four lines at once, sending four lines of garbage to his opponent.
 Garbage In-Depth
Games with random garbage, like Tetris Worlds, will mathematically output two aligned garbage holes (an easy double) 1:10 garbage lines, three aligned every 1:100, and four aligned every 1:1000.
Some games, like Tetris DS feature semi-random garbage output. With random garbage, the player will receive at least a double's worth of aligned holes 10% of the time. Empirical data suggests Tetris DS leans closer to 72%.
Early games like Tetris (Game Boy) will switch the garbage's hole column every nine rows or so.
Some players prefer pure random garbage because aligned garbage tends to "see-saw" back and forth wildly. Others enjoy the depth and challenge presented by random garbage.
Tetris Worlds is currently the only game which lacks retaliation garbage, meaning clears from garbage will not send back any garbage. Because of this, clearing garbage becomes less desirable, which a player may argue deprives the game of some depth.