Hemp, in a word. Some other stuff, like linen/tow, but not very significant. Ships of the time were dependent on hemp. George W. grew it.
Search out "rope walks" to learn how and where it was made. These days mostly you'll find three-strand right-laid rope. Four-strand was used as well. In the 18th century both right- and left-laid rope was made. Replica ships today use synthetic look-alike stuff, almost all three-strand and right-laid. I'm given to understand that ships then used one lay on the starboard side and the opposite lay on the larboard. Can't remember off the point of my brain which was which.
You can still get hemp rope in a variety of sizes. Sisal and manila are new stuff, and nowhere as good. One fella's opinion.