Notion of manifold is often motivated today by examples of simple surfaces, including developable ones, so this is a natural guess, but it is unlikely to be the case historically. German Mannigfaltigkeit is associated not so much with geometric folding as with "many folded into one", alternatively translated as "multiplicity". Cantor even used Mannigfaltigkeit for general sets until 1890s, when he switched to Menge (literally "quantity"), although according to Husserl "this conception does not coincide with that of Riemann and as used elsewhere in the theory of geometry, according to which a manifold is a collection not of merely united, but also ordered elements, and on the other hand not merely united, but continuously connected elements".
Riemann himself in his lecture uses Mannigfaltigkeit as almost synonymous with "magnitude", saying that he set himself "the task of constructing the notion of a multiply extended magnitude", and invokes different intuitions when first using the word, Mannigfaltigkeit can equally be discrete:"according as there exists... a continuous path from one to another or not, they form a continuous or discrete manifoldness; the individual specialisations are called in the first case points, in the second case elements". He is also quite clear on his influences:"besides some very short hints on the matter given by Privy Councillor Gauss in his second memoir on Biquadratic Residues, in the Gottingen Gelehrte Anzeige, and in his Jubileebook, and some philosophical researches of Herbart, I could make use of no previous labours". Herbart is a German philosopher who clarified and popularized Kant's philosophy of space, he also influenced Grassman and his "science of magnitude".
The motivation he cites is related to complex analysis:"Such researches have become a necessity for many parts of mathematics, e.g., for the treatment of many-valued analytical functions; and the want of them is no doubt a chief cause why the celebrated theorem of Abel and the achievements of Lagrange, Pfaff, Jacobi for the general theory of differential equations, have so long remained unfruitful". Finally, the main focus of the lecture are local metric properties of manifolds, especially curvature, but developable surfaces are folded from flat ones, i.e. they are locally flat and have zero curvature. So they wouldn't be interesting for what Riemann has in mind.
