"serving as a model; worthy to serve as an exemplar," 1844, from model (n.). Model railway is by 1864.
1570s, "likeness made to scale; architect's set of designs," from French modelle (16c., Modern French modèle), from Italian modello "a model, mold," from Vulgar Latin *modellus, from Latin modulus "a small measure, standard," diminutive of modus "manner, measure" (from PIE root *med- "take appropriate measures"). Sense of "a standard for imitation or comparison, thing or person that serves or may serve as a pattern or type" is from 1630s.
If the Model Boy was in either of these Sunday-schools, I did not see him. The Model Boy of my time—we never had but the one—was perfect: perfect in manners, perfect in dress, perfect in conduct, perfect in filial piety, perfect in exterior godliness; but at bottom he was a prig; and as for the contents of his skull, they could have changed place with the contents of a pie and nobody would have been the worse off for it but the pie. ["Mark Twain," "Life on the Mississippi," 1883]
Meaning "motor vehicle of a particular design" is from 1900 (such as Model T, 1908; Model A, 1927; Ford's other early models included C, F, and B). Sense of "artist's model, living person who serves as the type of a figure to be painted or sculpted" is recorded by 1690s; that of "fashion model" is from 1904. German, Swedish modell, Dutch, Danish model are from French or Italian.
c. 1600, "describe in detail" (a sense now obsolete); 1660s, "fashion a figure or imitation (of something) in clay or wax," from model (n.). Earlier was modelize (c. 1600). From 1730 as "construct or arrange in a set manner." From 1915 in the sense "to act as a fashion model, to display (clothes)." Related: Modeled; modeling; modelled; modelling.
late 14c., "original model of the universe in the mind of God," later (mid-15c.) "model of virtue," from Old French exemplaire (14c.) and directly from Late Latin exemplarium, from Latin exemplum "a copy, pattern, model" (see example). Related: Exemplarily.