It is a natural chemical precipitate of carbonate minerals; typically aragonite, but often recrystallized to, or primarily, calcite.

Travertine forms as calcium carbonate is deposited from the water of mineral springs or rivulets that are saturated with dissolved calcium bicarbonate. The spring water from which the calcium carbonate precipitates can be hot, warm or cold. The rate of deposition increases with the temperature of the water, or alternatively, when biotic material accelerates the process of precipitation.
In Arizona a lot of the redwall and escabrosa limestones are dissolved out to make the travertine deposites such as in Fossil creek, Havasupi canyon, and Kartcher caverns.