Simple really. The lines are are a living or nonliving things "death". As for the points they are the Point of Death for said living or non-living thing.
To put it in simpler terms it's basically showing what line or point to attack to kill your target. The only problem is that it can be very dangerous to constantly see the lines and points of death 24/7 since it can drive a person mad. Also, it seems to obtain it is to manage t survive a near death experience and be possibly from one of the four deamon hunter clans that were mentioned in Tsukihime and/or Kara no Kyoukai.
In any case Tohno Shiki uses this to follow the lines and go for the points, while Ryougi Shiki is more skilled with her Eyes since she had the proper training for them.
- Finding my way through this garden is rather unbearable, but if it is to keep the one I adore company I will endure it for her sake, and her sake alone.