Poland and Lithuania had a personal union under Sigismund II. A personal union means that two countries share a monarchy, such as Austria-Hungary having the Empire of Austria and the Kingdom of Hungary as two separate entities, ruled by one person who was simultaneously the Emperor of Austria and King of Hungary.

Around the time of the Union of Lublin, Lithuania was under severe pressure from the Russians. However, the Polish nobility didn't really want to help without some sort of concession from the Lithuanians. Sigismund decided to try and manipulate the nobles to agree to join the two countries into one, which was achieve at the Union of Lublin. However, when Sigismund died without an heir, it was decided to have the nobles of Poland-Lithuania elect the next king-thus rendering the Commonwealth an elective monarchy. And that structure remained the system of the Commonwealth until its eventual dismemberment.

The problem with the structure is that, while granting a large number of liberties to the nobles allowed for the elections to take place mostly undisputed, the nobles often acted autonomously and would feud with each other and the king. Often times the king's military was essentially limited to his personal levy and whatever his allies would be able to dig up. There was also a clause in the Polish Parliament, the Sejm, that required all the nobles to agree on legislation. This resulted in what was known as a liberum veto, where any noble could veto any legislation single-handedly. Foreign influenced nobles (from Prussia, Austria, and Russia) often invoked this veto whenever Poland tried to reform, thus preventing any real internal change or development.

Meanwhile, Poland's foreign policy was in chaos. After a failed attempt to add the crown of Russia to the Commonwealth, Poland experienced a time of instability. Ukrainian cossacks revolted against the Poles and swore loyalty to the Russians, resulting in an extremely costly war that depleted the Polish military. Meanwhile, Swedish troops swept into Poland proper, sacking and burning valuable and wealthy Polish territories, in what became known as the Deluge. The result was a severely weakened Commonwealth that became easily manipulable by its neighbors, which eventually resulted in the Partitions of Poland by Prussia, Austria, and Russia.

The Winged Hussars were primarily effective because of their military discipline and the fact that they were superior cavalry to most other countries at the time. For instance, at the Battle of Kircholm, the extremely strong and disciplined Swedish army was routed within half an hour by a massive Polish cavalry charge despite outnumbering the Poles by more than 2:1. The Swedish cavalry simply didn't have the power to engage the Polish lancers and shattered, exposing the infantry's flanks and causing a total collapse of the line. This battle among others inspired the Swedes to change their cavalry tactics from the sword and pistol reiters to lance equipped chargers. However, the main disadvantage of the hussars was that due to the need to maintain powerful war horses, only some of the Polish nobility, or szlachta, were able to maintain them, thus limiting their numbers and use. In addition, as infantry rate of fire started to increase, cavalry as a whole became less effective, especially the frontal charges favored by the Poles.

After World War I, both Poland and Lithuania received independence from Germany and Russia. However, the two quickly got involved in a border dispute over the city of Vilnus/Wilno. This sparked a war between Poland and Lithuania, which Poland won, securing both Vilnus/Wilno and the Suwalki region for Poland, and earning the ire of the Lithuanians. Specifically, the Polish leader, Pilsudski, was born in Wilno, and arranged a military seizure of Vilnus by a group of so-called Polish mutineers that declared independence from Lithuania and held a "referendum" to join Poland. This did not go over well and polluted Polish-Lithuanian relations for some time.

Sources:

Frost, Robert. After the Deluge: Poland-Lithuania and the Second Northern War

Davies, Norman: White Eagle and Red Star