Silvertone was the brand given to musical equipment sold by the legendary Chicago retailer Sears, Roebuck and co. They sold guitars in huge volumes at significantly lower prices than the better known US brands, and although naturally not of equivalent quality, are still largely valued by collectors and musicians to this day. Most musicians who learned to play in the fifties and sixties will have had a Silvertone pass through their hands, and it is perhaps this nostalgia that keeps interest levels high.
Sears were, of course, a longstanding catalogue retailer, and had offered musical instruments at least as early as the 1920s, and guitars from the 1930s. The first solid body guitars appeared in 1954 - models 1361 and 1363 - really not long after the early solid body offerings of Fender and Gibson.
Sears did not produce instruments themselves; most Silvertone guitars were made by other American,(quite often Chicago) companies. Early guitars were produced by Danelectro (eg models 1375, 1377, 1303/U2, 1448, 1449) who had been making Silvertone amplifiers since the 1940s. Later guitars were produced by Harmony (1429), Kay, Valco and, later still, Teisco. Many of these guitars were direct analogues of instrument offered by the maker - such as Harmony's H19 Silhouette or the Kay Thin Twin, others were made exclusively for Silvertone.