The nobility of the Polish-Lithuanian commonwealth did indeed elect their kings and many thousands of nobles would have been eligible to vote in the election. Anna Grześkowiak-Krwawicz estimates that the noble estate constituted approximately 6-8% of all the inhabitants of Polish and Lithuanian lands--a percentage much higher than the noble estates of other European countries like France.

In the eighteenth century, faced with a political crisis and burdened by a political system that had not developed modern representative bodies like other Western European nations, several political reformists commented on the oddity of this practice. Jean-Jacques Rousseau, for one, wrote a lengthy proposal to streamline the legislative and electoral institutions of Poland. Willmoore Kendall's introduction to Rousseau's The Government of Poland gives some idea of the unwieldy nature of the election assembly or sejm:

By long established custom the Poles elected their kings. Moreover, since on the face of it the choice of a new king, upon the death of his predecessor, did not lend itself to imperative mandates, the Polish nobles refused to entrust the king's election to the Diet. Rather…they insisted upon being present in the flesh at the elections and casting their votes personally…The mind boggles as it attempts to conjure up the spectacle: several hundred thousand electors, each with a vote that, again by immemorial custom, was as 'good' as that of every other man, assembled in one place…

As anyone among the nobility could be elected and they counted their attendance among their "rights and liberties" huge numbers would have been present. Jacek Jędruch estimates it at anywhere between 10,000-100,000. The voting along could take several days and to accommodate the huge crowd sizes typically met in Wola, near Warsaw. The process could also be incredibly contentious and in some instances the election of non-Polish monarchs made it prone to outside influence and led to instability. For instance, in 1573, the Polish nobles elected the future Henri III of France to serve as its king over the objections of the Lithuanian nobles. However, only two years later, when Henri unexpectedly inherited the throne of France, he resigned, provoking a constitutional crisis in Poland. If you are interested in what the sejm looked like visually, there are also several artistic representations of the assembly that elected Henri III.

By the late eighteenth century, numerous authors recommended that Poland do away with the free election and adopt a hereditary monarchy so as to remedy the inefficiencies of this system. Rousseau actually advocated the opposite and recommended that the nobility instead expand enfranchisement. Either way, the Constitution of 1791 did away with the election and established a constitutional monarchy, before Poland fell subject to Russian invasion shortly thereafter.