Those 4 white boxes form a shape
or a tetromino
You launch this shape from the bottom field into the upper main game field. The shape should hit any white box on the upper field, otherwise it'll fly through and you lose points. Also the shape should not stick out of the field, or the game will be over.
The goal of the game is to build complete lines (horizontal or vertical) with white boxes. When you complete a line, it disappears, clearing the space for new shapes.
In original Tetris you can control shapes (move and rotate) and that's it. While in Doptrix you control both the shapes and the game field, which makes the game much more complex and interesting.
Sorry, my English is not very good, I wish I could explain better : )