It took awhile to figure out that the above item washed up on our beach was a brown alga of the genus TURBINARIA. Turbinaria tricostata is listed as a common species off the Quintana Roo coast, so maybe it's that one. The genus Turbinaria resides in the same family as better-known Sargassum of Sargasso Sea fame. That makes sense because the two genera produce species of similar color and display the same living strategy of floating about in loose, chainlike clusters. The genera are members of the order Fucales, and are known as Brown Algae.
There's a good bit of info on the Internet about the use of Turbinaria species medicinally. A quick scan turns up papers using a species from the Yucatan coast against the Leishmania parasite, and there's another page describing its antioxidant activities.
From what I can read, Turbinaria species can reproduce either sexually or by fragmentation -- small pieces of it "rooting" on submerged rocks. And anything producing such huge amounts of biomass as I saw heaped on the beach that day, just hinting at what remained out in the ocean, is bound to have enormous importance to the oceanic ecosystem.