It is a compound of the terms rzecz "thing, matter" and pospolita "common", a calque of Latin rés pública (rés "thing" + pública "public, common"), i.e. republic, in English also rendered as commonwealth (historic) and republic (current).
It was adapted for Poland, as it at that time had a unique republican system, similar to the former Roman rés pública.
The famous quote by Jan Zamoyski, the Lord Chancellor of the Crown, on the importance of education is an example of its use: Takie będą Rzeczypospolite, jakie ich młodzieży chowanie.
As a result, the literal meaning of Rzeczpospolita Polska is "Polish Commonwealth", or "Republic of Poland".
Although the first Rzeczpospolita was an elective monarchy, the king had no real power, as most of the state affairs were regulated by the parliament and senate, known as the Sejm.