Kevlar is poly para-phenyleneterephthalamide. That structure has a benzene ring that has a carbon chain on each opposite end ("Para") in a repeating fashion. So, it is like a strand of a rope.
The strands are held together tightly by hydrogen bonding between the amide (carbonyl (C=O) with an amine (NH) on one side) and by stacking interactions between the benzene rings and (a little bit) by dispersion forces.
So, since the strands hold on tightly to each other, it is chemically "tightly woven".