When we chant, we usually burn three sticks of incense, but if too much smoke is produced we may use fewer. The three sticks of incense represent the three treasures — the treasure of the Buddha, the treasure of the Law, and the treasure of the priesthood. The treasure of the Buddha is Nichiren Daishonin. The treasure of the Law is the Dai-Gohonzon. The treasure of the priesthood is Nikko Shonin and the successive High Priests.
When we use incense sticks for secular purposes, we usually burn them in an upright position. In Nichiren Shoshu, they are laid down. The significance behind this is that when the incense is standing upright, the ashes fall and scatter. The scattered ashes signify a scattered mind. When the incense is laid down, the ashes do not scatter. It also purifies the area in front of the altar and is an offering to the Gohonzon.