it had patches, and these were a not very important technical first, because an artist could create the same geometry in a number of ways and get the same end result. from a usability perspective of level editors though, it saved the environment artist a considerable amount of time, effort and risk of mistakes.

the patches were cubic bezier patches of fixed subdivision. other game engines improved on this in short order to have dynamic subdivision/lod based on distance without cracks and more complicated patch types (e.g. you can never make a sphere with quake 3's patches)... whereas keeping the subdivisions fixed means that cracks are trivial to avoid.

i believe that quake 3/id tech 3 did not solve this even in later iterations... it was more another tool to add fixed, un-lod-ed triangles to the environment mesh, with an added caveat that they didn't seal the convex hulls describing the pvs and inside/outside or get used to provide planes to split the bsp.