Refers to a sword that cuts well. Often used figuratively in phrases like 快刀乱麻 (cutting through difficulties decisively).
He cut the bamboo in two with a single stroke of his sharp sword.
He solved the problem with a decisive, cutting-through-the-Gordian-knot decision.
cutting through difficulties with decisive skill
快 (pleasant, sharp) + 刀 (sword). The combination straightforwardly means a sharp, well-cutting sword.