About coconut fiber armor:
The coconut fiber armor is most likely Polynesian or Micronesian, and the weapon has shark-teeth edge. I would assume that these materials were used just because there was nothing better available.
About modern armor:
When nylon and kevlar body armor become first available (1970's), they were designed to resist bullets which will deform and flatten on impact. This deformation spread the impact on larger area, and the impact was received by a large number of kelvar fibers. When the armor was hit with non-deforming projectile, such as armor-piercing bullet or metal blade, the impact was received by a small number of fibers. Some reports claimed that a light kevlar vest is as good as thick leather coat against stabbing.
Modern body armors have been designed to handle both bullets and blades, and have both "ballistic resistance" and "stab resistance classification". The stab resistance is further divided into "blades" and "spikes" -category. Blade resistance describes how well the armor can withstand stabs from properly made sharp-edged blade, and spike resistance describes the resistance against improvised thrusting weapons, such as sharpened screwdrivers.
Note: Bad movies and sloppy journalism have caused several bad misconceptions how bullets and targets behave. When I was in university, our professor's office had a signboard reading "You must know at least this much about terminal ballistics before you can talk to me", and an arrow pointing to a shelf with all issues of "International journal of impact engineering".