Garbage is a form of "attack" in multiplayer Tetris that has been around since the days of the NES. The basic gist of it is that if you clear multiple rows of blocks at one time, extra rows get added to the bottom of your opponent's screen.
The gabrage system is simple. The more rows you clear at once, the more garbage rows are sent to your opponent:
|Number of rows cleared||Number of rows sent|
|1 row||0 rows|
|2 rows||1 row|
|3 rows||2 rows|
|4 rows||4 rows|
However, in Tetris DS, the garbage system is changed so that the number of rows sent to your opponent is proportionally increased over the course of the game.
Top screen is Player 1's and bottom is Player 2's.
If Player 1 drops the "T" here:
It will clear two lines at once, sending one row of garbage to Player 2:
Then, if Player 1 drops the "4-Bar" here:
It will clear 4 lines at once, sending four lines of garbage to Player 2.