As captain, your main goal is to keep the ship fueled as it races in pursuit of Hell Metal. You ship is fueled by the energy created by joining cubes, which is where the puzzle element comes into play. The basics behind the whole thing are pretty simple; blocks fall from the top of the screen, which you must combine into 3x3 squares.
These squares can then be combined with other squares, creating larger squares. Unlike other puzzle games involving blocks, you job in Trioncube is to create the biggest squares you can. As you combine squares, they will set off combo chains. When the combo ends, they convert into points which are needed to move to the next level.