See also, Cuttings, Budding...
Own root roses are roses grown from cuttings and grown on their own roots, rather than budded to a rootstock.

[From Peter Schneider on Roses, by Peter Schneider, pp. 82-4:] While a mature hybrid tea plant grown from a cutting will produce the same size blooms as a bud-grafted plant, this is not the case with miniatures. All of the varieties introduced from Europe as patio roses are bud-grafted onto a rootstock, and [Schneider is] certain that more than a few of them would shrink to miniature proportions if they weren't... almost all American-raised miniatures are sold on their own roots, and many of them could be expected to gain greater size -- in both the bush and the bloom -- as budded plants...

[From The Practical Book of Outdoor Rose Growing, by George C. Thomas, Jr., p. 21-2: The author, writing in 1915, tells about an experiment he conducted to determine which method was preferable.] One bed was made, and over fifty roses on their own roots and fifty budded roses were planted in it side by side, all of old and established varieties, and, in the case of the own root plants, purchased from a grower who advocates their use. At the end of the first summer the difference was plainly apparent and was strongly in favor of the budded plants. At the end of two years there was no possible doubt as to the result; the budded plants were far superior. Experiments with other roses have endorsed this result, and budded roses are recommended for all outdoor work for the majority of roses contained in [the author's] main list, whether Hybrid Teas, Hybrid Perpetuals, or Teas.

[From On Their Own... And Growing Well, by Dick Streeper, p. 24:] hybrid tea roses and many types related to them display a lack of uniformity in size and vigor [when grown as own-root plants... many] varieties when budded onto [understocks], grow with a high degree of uniformity... Hybrid tea roses are quite difficult to grow with good uniform vigor as own-root plants... Miniature roses have always been grown on their own roots... As a general rule, roses which tend to grow upright do not do well as own-root plants and those which grow laterally produce good own-root plants...