Short answers, pulled from the story.
Golden Liberty was the political system of the Kingdom of Poland and, after the Union of Lublin in 1569, the Polish-Lithuanian Commonwealth, under which all nobles held equal legal status and controlled the Sejm and the elected king.
Only male szlachta held political rights under Golden Liberty, described in one estimate as about 15 percent of the population and in another as about 10 percent. Either figure was still a far larger share than held political rights in most other European countries of the time.
Liberum veto was the right of a single land envoy in the Sejm to block a majority decision, and using it nullified all legislation passed at that session. During the crisis of the later 17th century, nobles also began using the liberum veto in provincial sejmiks.
Golden Liberty declined because liberum veto and other abuses paralyzed government, the szlachta refused to fund a larger modern army through taxes, and magnates bribed by foreign powers blocked political action. The Commonwealth could not keep pace with more militarized neighbors and was partitioned and annexed by stronger absolutist countries in the late 18th century.
Golden Liberty has been described as a precursor to modern democracy and constitutional monarchy, since the Sejm could veto the king on legislation, war and taxation. Because the Sejm usually vetoed a monarch's war plans, the system has also been cited as an early argument for democratic peace theory.
Critics say Golden Liberty excluded peasants and townsfolk from legal protection, contributing to slow growth in Commonwealth cities and the spread of the second serfdom among peasants. The Commonwealth was called Noble's Paradise but also Purgatory for the Townsfolk and Hell for the Peasants, though some Russian peasants fled harsher lords to settle in Poland instead, which is cited as counterevidence to the harshest of those labels.