After giving birth to two daughters Hedwig of Sagan, fourth wife of Casimir III*, King of Poland gave birth to long awaited son. Vladislaus (Władysław), born in 1369, was first royal son born in Poland from the time of his father's birth almost 60 years earlier**. Although Casimir's second wife, Adelheid of Hesse, was still alive, so validity of King's marriage with Hedwig was questionable, subjects of Casimir has seen little Vladislaus as their fully legitimate heir. Birth of Piast*** prince closed road to the Polish throne for Casimir's nephew, Louis of Hungary. Although birth of son made Polish King very happy, it also made Polish-Hungarian relations cooler. Hungarian support in planned war against Luxembourgs was not that certain now.
*Casimir the Great never used that number, on coins from the time of his reign he is Casimirus Primus . Later historians counted him as third Casimir on Polish throne, although neither Casimir the Restorer nor Casimir the Just were Kings. Still, it is not impossible, that ITTL historians centuries later would also give him that number, so let's call him Casimir III anyway.
**IOTL Poles waited for Royal son much, much longer. After Casimir III first male heir was born to Polish King in 1424, after 114 years. King leaving surviving, legitimate sons remained rarity for centuries, out of 15 Kings, who ruled Poland between 1333 and 1672, only 4 left legitimate sons, who outlived them. That was Miracle of House of Capet in reverse.
*** Piast as name of Dynasty is also anachronism (like most of dynasty names of the time). It was used only by the last Silesian Piasts-17th century Dukes of Legnica/Liegnitz.