In the Hebrew Bible there was division between these two books, which were part of a series (including 1 and 2 Kings, 1 and 2 Chronicles) that traces the origin and development of kingship in Israel. The two books of Samuel follow the rise of the person who has been given the most space in the Old Testament—David.
What was so special about this one person in Jewish history? He is the most famous Hebrew king (he conquered a lot of territory), he gave the city of Jerusalem to Israel (it became, like Washington, D.C. to Americans, a central city to unify northern and southern peoples), he wrote beautiful poetry (many of the psalms), and he became the focus of hope in a Messiah who would some day save his people.
The books trace the beginning of kingship in Israel—Samuel’s life (1 Samuel 1-7), Saul as first king (1 Samuel 8-15), the rise of David (1 Samuel 16-31), David as king over Judah only (2 Samuel 1-4), David as king over all Israel (2 Samuel 5-24). The time period roughly covers the years from 1100-1000 B.C.
Note that the concluding comments at the end of Samuel (2 Samuel 24:18-25) discuss the process through which David bought a threshing floor and erected an altar there; this site will later become famous as the location for Solomon’s glorious temple and the current Moslem Dome of the Mosque.