Before the First Book of Kings there was only one nation - Israel named after Jacob (whose other name was Israel and who was called the Father of Israel). But in the Second Book of Kings it is not Israel anymore, there are Israel and Judah. When did that separation happen? There were 12 Israel's knees before the Kingdom of David but then Judah's knee is emphasized separately. Why is that?
Shlomo ("Solomon"), the son of David, continued to go whoring after gods other than YHVH (1 Kings 11:1-10). This was exacerbated by his numerous foreign wives of whom God warned Shlomo that they would cause him to go astray and commit idolatry.
Consequently, YHVH told Shlomo that he would rend the kingdom from him, except that He would leave one tribe (the tribe of Yehuda) under his dominion on account of Shlomo's father, David, who was a man after God's heart.
God also informed Shlomo that the split would not occur during Shlomo's reign, but during the reign of his son, Rechav'am ("Rehoboam"). Read 1 Kings 11-12 for all the details.
Since that time, the kingdoms have remained apart. The northern kingdom was called by various names, including Yisra'el ("Israel"), Shomron ("Samaria"), Efraim ("Ephraim"), Yosef ("Joseph"), while the southern kingdom was called Yehuda ("Judah").