Two leading theories:
Christopher Columbus, on his fourth voyage (1502), reportedly exclaimed "Gracias a Dios que hemos salido de estas honduras!" ("Thank God we've left these depths!") after surviving a storm off the coast. The name stuck for the region's deep coastal waters.
Some suggest a blend of Mayan hun ("one") and Nahuatl duras ("strong"), implying "one strong [people/land]." This lacks strong documentary support.
The Spanish nautical term "honduras" (depths) is the widely accepted etymology, referencing the deep waters near the Caribbean coast.