Polish-Lithuanian Union was created in 1385 in the city of Krewo, and then further expanded by later unification procedures. This later led to the creation of much more unified Polish–Lithuanian Commonwealth in 1569.

The main reason why the union was brockered in the first place, was the common threat that both Lithuania and Poland faced, in the form of aggresively expanding Teutonic Order.

The Teutonic Order was invited to take land in what is today northern Poland, in 13201226 (edit: I wrote 1320, meant 1230, and it was 1226 in reality), in order to pacify the unruly and agressive Pruss tribes that menaced the Polish Kingdom, as well as aid in the christianisation of Lithuania. However, the christianisation of Lithuaina took pplace soon after, in 1387, and the Pruss got conquered and assimilated into the caste system of the Order, stripping the Order of its main purpose and reason to exist.

This in turn, forced the Order to separate itself form its former mission, and instead expand as a semi-feudal enterprise, with only a paper-thin pretense of missionary work. In less than 60 years since its arrival to the Baltic shores, Teutonic order become a main threat to the very existence of Lithuania, and political independece of Poland.

In 1385, Lithuanian Grand Duke Jogailla (pronounced Yogaiwwa) married the Polish King Jadwiga (pronounced Yadviga, she was female, but her official title was that of a king, not queen), Jogailla then assumed the name of Władysław (Vladiswav) I Jagiełło (Yaghiewwo) King of Poland. This cemented Polish-Lithuanian Union of both the state, and the crowned heads, and since then, and created a common front against the Order.

Even after the subsequent defeat of the Order, Poland and Lithuania remained politically and culturally united. Countless people migrated back and forth between the two states, and large part of the nobility intermarried.

It is worth noting, that the most famous icon of Polish culture, the epopeic poem "Master Thaddeus" starts with:

"Lithuania, my country! You are as good health: How much one should prize you, he only can tell Who has lost you."

This clearly shows that at least up to the late XIX century, there was a great cultural bond between those two countriesd and cultures, to the point that for many Poles at least they were BOTH the fatherland.

Sources:

"Master Thaddeus" Adam Mickiewicz

S.C. Rowell. "Lithuania Ascending"

O. Halecki, "Dzieje unii jagiellońskiej w wiekach średnich" (the history fo the Jagiellonian Union in the Middle Ages)