All he did there was he chose an edge loop that ran the length of the entire shape, selected all the vertices, SHIFT+D to duplicate those vertices as well as the edge loop, then extrude a new surface from those duplicated vertices. It would be exactly the same if he was in edge mode, selected one edge loop, duplicated it, then extruded a new surface from that duplicated edge loop. It's the same process in vertex mode. When he said "grab the curvature", he's referring to the edges and vertices that make up the profile curve of the shape. That is the long edge loops that run from "north to south" on the model.

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