Tanjiro's compassion in the world of demon slaying is significant because it sets him apart from other demon slayers who typically approach their mission with anger and hatred towards demons. Tanjiro's compassion allows him to see demons as beings capable of redemption and understanding, leading to instances where he tries to find peaceful resolutions rather than just resorting to violence. This compassion not only helps him develop deep connections with others but also influences those around him, showing that empathy and understanding can have a powerful impact even in the midst of darkness and conflict.