Carrageenan is made from seaweed (so it's natural and vegan-friendly). Most of the carrageenan used in commercial products comes from farmed seaweed, not seaweed found in the wild.
Farmers tie seaweed "cuttings" or "seeds" to lines and the seaweed grows around the line. It can then be harvested, dried (normally by the sun), and then sold to be processed into carrageenan.