From what I understand it was a powerhouse of Europe, but eventually was wiped off the map for centuries. What happened? How? Why?
Gradual destabilization and loss of the political power was a relatively long, complex process, although the chief reasons for this decline could be chalked up to the specific internal politics of the Polish-Lithuanian Commonwealth that merged rather anachronistic form of feudalism with democratic institutions, to a large extent modeled on those used in ancient Greek states, emergence of strong contenders to the power in Central Europe between late 16th and early 18th century, and the extremely serious toll taken in wars fought within the territory of the Commonwealth throughout entire 17th century and early 19th century.
Aforementioned combination of largely feudal economic system with a limited form of a representative democracy, was one of the reasons behind the eventual fall of the Polish-Lithuanian Commonwealth, although the weaknesses of such a system were not the direct cause of the decline, but rather exacerbated problems that have arisen in 17th century. Some historians point out that the establishment of conservatively feudal economic system possible through the very strong political position of the lower and middle nobility was problematic by itself, as strong political position of the noble class, complete with a relatively weak position of royal court severely hindered development of an efficient (not necessarily strong) central government and an early equivalent to a middle class (what adversely influenced the urbanization rate). In other words, until late 18th century, Polish-Lithuanian Commonwealth remained largely agrarian confederation of private, self-governed domains whose rulers were gathering together to discuss the governance of the entire province and elect representatives to the countrywide parliamentary sessions. Such model of governance fueled distinctly conservative attitudes that caused the lack of new reforms at a statewide level more desirable than the emergence of new laws that, although beneficial to a country as a whole, were usually considered detrimental to the nobility itself.
The institution of afree veto (lat. liberum veto) is sometimes presented as an element instrumental in the eventual collapse of the Polish sovereignty, but this opinion, quite common in 20th century historiography, especially among the followers of so-called Cracow School of History, is now considered too simplistic. Liberum veto is now considered a product of the general political landscape of Poland and Polish-Lithuanian Commonwealth that created a milieu that did not stand the test of time as a whole. In essence, liberum veto allowed any representative to render the parliamentary session null, along with all the decisions made until that point, causing the new acts to be accepted by total acclaim rather than a majority vote. As early parliament was a convocation of the representatives of particular provinces, each of said representatives was responsible for ascertaining that all the decisions will favour his electors, i.e. nobility from a given region, so that some regions won't get preferential treatment at the expense of others. It is worth noting that this mechanism was seen as inherently risky from the start, yet it worked very well, given that it has been already in use in late 15th century, while the first parliamentary session to be cancelled by the free veto took place only in 1669, after almost 200 years of using this principle (you might find the date 1652 in some sources, but this was the case of vetoed proposal to prolong the session over the usual time limit).
The crisis of 17th century was to large extent caused by the participation of Polish-Lithuanian Commonwealth in many conflicts, from the Polish-Swedish wars with the extremely destructive Second Northern War of 1655-1660 (its death toll being compared to Black Death), Polish involvement in Time of Troubles in Russia around 1610 and multiple Cossacks' uprising with the largest one being led by Bohdan Khmelnytsky's in 1650s to the wars with Ottoman Empire in later decades of the century. Widespread destruction impoverished large number of the lower nobility forming the vast majority of the Estate, what increased the disparity between average nobles and the wealthiest, most influential families. This led to the informal consolidation of power in the hands of relatively small group of the magnates, who were able to lure and bribe large number of poor nobles to their cause, essentially creating a oligarchic clientele system, drastically decreasing the effective number of factions in the parliament, as particular representatives started to support their patrons rather than their own lands.
It is sometimes posited that this situation was not dangerous as such, because it could have, paradoxically, lead to much higher level of political cohesion within the country. The problem was that the aforementioned magnates were not above collaboration with the foreign powers that, quickly developing since late 16th century understood the chance it allows them and began to actively interfere with the affairs of the Polish and Lithuanian magnates to maintain the political chaos in Poland as long as possible, at the same time building a completely different, absolutist form of government in their own territories. In addition, the idea of royal election, in theory decreasing a possibility of dynastic rule that could have increased the monarch's position, although, again, not destructive by itself, allowed not only local but also foreign candidates, causing 7 out of 11 elected monarchs to come from foreign countries. Such kings were often more interested in pursuing political goals in their lands of origin, dragging the Commonwealth into additional conflicts. Such process eventually contributed to the lack of stable relationships with other powers, depriving the Commonwealth of any reliable allies and isolating it politically. To make matters worse, several kings of 18th century tried to grant various privileges to all important factions more or less equally to appease all of them, what, incidentally only strengthened a political impasse. In such milieu, the very institutions and mechanisms developed to keep the democratic system in a relatively loose federation of large, diverse noble class and prevent the rise of absolutist monarchy became widely abused by the small number of immensely powerful political factions.
Thus, in the first decade of 18th century, comparison between Polish-Lithuanian Commonwealth and their immediate neighbours was almost an inversion of the political landscape of central and eastern Europe a hundred years ago. Weak, divided Russia suffering a power vacuum was replaced by quickly developing, centralized modern state during the reign of Peter I. Prussia, a vassal state to Poland became a dangerous contender in the north, having practically gained independence in 1657. In the late 16th century the prospect of a real union between Polish, Lithuania and Sweden after the election of Sigismund Vasa to a Polish-Lithuanian throne, although rife with problems, was certainly possible while during the Great Northern War in the first two decades of 18th century, Swedish army moved unhindered through the territory of the Commonwealth despite lack of formal consent of the rulers of the latter. While around 1600 Poland had a real chance to influence the politics in e.g Russia or Prussia, in early 1700s the struggles between Polish and Lithuanian magnates were used by neighbouring countries to further weaken the Commonwealth. Between 1720 and 1732, Russia, Prussia, Ottoman Empire, Sweden and Austria made several pacts, where they agreed to keep the political status quo in Polish-Lithuanian Commonwealth, counteracting any possibility of reforms that could have improved situation in the country.
So, to sum it up, a strong position of nobility and the democratic institutions consolidated a relatively archaic economic system and a loose political organization that survived well into 18th century. Losses suffered throughout the 17th century wars impoverished large number of decision-making nobility, shifting the power towards small group of most influential people who used that to further their own goals to the detriment of the country as such. Lack of political allies and increasing power of the neighbour states made it easier for the latter to cooperate against the Commonwealth, slowly turning this former local powerhouse into a 'sick man of Europe'.