Players try to connect sets of four blocks so that their colors match, causing the blocks to be removed. Remaining blocks may then fall and complete other sets of four blocks. The main difference between Tecmo Stackers and Puyo Pop is that blocks in Tecmo Stackers stretch in various directions after adjacent blocks are removed, and the "arms" they send out can complete sets of blocks and be removed; this allows for longer chain reactions.
In arcade mode, players try to keep their stack of blocks from reaching the top of the screen. Long chain reactions send blocks to the opponent's screen. Arcade mode is available for one or two players, with players able to choose their difficulty independently of one another. Chain reaction mode centers on getting as many chain reactions as possible. In time trial mode, players try to keep their screen from filling with blocks for as long as possible.
Source: Wikipedia, "Tecmo Stackers", available under the CC-BY-SA License.