The YouTube video from "NFPA Joe" explains the three and four times rule, which is used in NFPA 13 to determine the proper placement of sprinkler heads in relation to obstructions. This rule ensures that sprinklers have enough space to develop their spray patterns and effectively control fires. The video details the specific calculations for both horizontal and vertical obstructions and highlights the differences in application based on the type of sprinkler head, the hazard occupancy, and the size of the obstruction.