Temporal finitism is the idea that time is finite. The context of the idea is the pre-modern era, before mathematicians had understood the concept of infinity and before physical cosmology.
The philosophy of Aristotle, expressed in such works as his physics, held that although space was finite, with only void existing beyond the outermost sphere of the heavens, time was infinite. This caused problems for mediaeval Islamic, Jewish and Christian philosophers, who were unable to reconcile the Aristotelian conception of the eternal with the Abrahamic view of Creation.
In contrast to ancient Greek philosophers who believed that the universe had an infinite past with no beginning, medieval philosophers and theologians developed the concept of the universe having a finite past with a beginning. This view was inspired by the creation doctrine shared by the three Abrahamic religions: Judaism, Christianity and Islam.
Prior to Maimonides, it was held that it was possible to prove, philosophically, creation theory. The Kalam cosmological argument held that creation was provable, for example. Maimonides himself held that neither creation nor Aristotle's infinite time were provable, or at least that no proof was available. (According to scholars of his work, he didn't make a formal distinction between unprovability and the simple absence of proof.) Thomas Aquinas was influenced by this belief, and held in his Summa Theologica that neither hypothesis was demonstrable. Some of Maimonides' Jewish successors, including Gersonides and Crescas, conversely held that the question was decidable, philosophically.