The term “telos” is typically used to refer to the purpose for some thing or some activity. Different historians would see different teloi (plural of telos) for the study of history. However, the two most commonly perceived teloi for history would be out of reach of historians.
One possible telos for the study of history is to understand the lives of people from the past. This is a common vision of what history is for today. Many historians want to understand what the lives of common people were like at various times in the past. This is something that is beyond the capability of historians. It is, of course, possible to gain some insights into how people lived, but historians will never be able to truly understand how people thought and what their lives were like.
A second telos for the study of history is to give us insights into what we should and should not do in the present. This is encapsulated in the saying “those who do not know their history are doomed to repeat it.” In this view, the purpose of studying history is to learn its lessons so that we can avoid making the mistakes of the past. This, too, is something that historians can never truly accomplish. They cannot be sure that they are drawing the correct lessons from prior incidents. They cannot be sure that the situations in the present are similar enough to those in the past for the lessons to apply. Thus, this telos is beyond the reach of historians as well.
Historians, then, can never truly achieve the goal of their discipline, but they can come close and they can learn important things in the process.