The dynastic union between the two countries (converted into a full administrative union only in 1569) is the reason for the common appelation "Poland-Lithuania" in discussions about the area from the late Middle Ages onwards. Two Jagiellonians also ruled Hungary and Bohemia, which briefly (1440-44) shared their king with Poland.
Jagiełło (originally Jogaila sometimes Jagiellon), Grand Duke of Lithuania and the founder of the dynasty, became king of Poland as Ladislaus II after converting to Christianity and marrying Jadwiga, second of Poland's Angevin rulers. The former Polish ruling house of Piast (c.962-1370) had ended with the death of Casimir III.
While the Jagiellons were hereditary rulers of Lithuania, in Poland the king was elected. So while Poland's nobles (the Szlachta) always elected a Jagiellon to preserve the Polish-Lithuanian alliance, the kings usually had to grant some new privileges to be elected.
The Jagiellon rulers (with dates of ruling Poland-Lithuania in brackets) were: