In this paper we will introduce the Terzina instrument, which is one of the two scientific payloads of the NUSES satellite mission. NUSES serves as a technological pathfinder, hosting a suite of innovative instruments designed for the in-orbit detection of cosmic rays, neutrinos, and gamma rays across various energy ranges. The Terzina instrument itself is a compact telescope equipped with Schmidt-Cassegrain optics. Its primary objective is to detect Cherenkov radiation emitted by Extensive Air Showers generated by the interaction of high-energy (> 100 PeV) cosmic rays with the Earth's atmosphere. Terzina represents a critical step forward in the development of future space-based instruments aimed at detecting upward-moving showers induced by tau-leptons and muons resulting from the interaction of high-energy astrophysical neutrinos with the Earth. In this paper, we will delve into the key technical aspects of the Terzina instrument, its capabilities, and its potential for detection.