In the book of Numbers (15:38-39), we read that the Israelites were instructed to "make for themselves fringes on the corners of their garments…that they shall look at it and recall all the commandments of the Eternal and observe them..."
Over time, this garment became a tallit, or prayer shawl. Since the instruction is to observe the fringes, the custom developed to wear a tallit at services taking place during daylight hours. The tallit is therefore worn during morning services and not at night. The exception to this rule is the night of Yom Kippur, commonly known as Kol Nidrei. The tallit, often made of a white fabric, has come to represent the sincerity of our repentance. So, yes one can wear a tallit to services the night of Yom Kippur. And, it is customary for those who wear the tallit to wear it throughout Yom Kippur, for all prayer services.
The Eternal One spoke to Moses, saying, "Phinehas, son of Eleazar son of Aaron the priest, has turned back My wrath from the Israelites by displaying among them his passion for Me, so that I did not wipe out the Israelite people in My passion." - Numbers 25:10-11