The simple answer is that braided thread is stronger than unbraided. The reasons for this are somewhat complicated. One of the simplist ways to visulaize an answer is that the process of braiding or twisting the threads adds length. Six inches of braid requires that each strand be significnatly longer than six inches of unbraided. This added length provides the opportunity for stretch. As the individual strands stretch, they absorb shock. To break a braided section, the weakness of the section would have to be evident in nearly the same place in each of the three strands. While individual threads tend to break more at their independent weakest points.
The science behind your answer is actually fairly complicated.
Google searching "physics of ropes" will help you find the more complicated physics.
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