Terra cotta is a ceramic based building material that was very popular from the late 19th century until the 1930s. This material was largely used on commercial buildings but you often find it in residential applications. This material can be glazed to match brick and limestone in color and often on commercial buildings is glazed. There are large concentration of buildings with terra cotta detail in Louisville Kentucky where it was popular on the many late victorian Mansions on 3rd and 4 th street in Old Louisville. Becasue it was in an urban environment prone to exposure to air pollution and chemicals often it will be deteriorated. The National Trust has a preservation brief on its maintenance and preservation. http://www.nps.gov/history/hps/tps/briefs/brief07.htm
The 1st example in the photograph is on Mass avenue in Indianapolis on a commercial building and is the colored glazed variety. The home is the Wentz Mansion in Louisville I used to live in and has elaborate detailing on the tower, windows and doorway.