After King Solomon, the kingdom of Israel was split into two separate kingdoms: Israel to the north and Judah to the south. The kings of Israel are all evil and the kings of Judah are a mixed bag of God-fearing kings and idol worshipping kings. Case in point, Hezekiah's father Ahaz is an evil king but Hezekiah turns out to be one of the best kings that Judah has throughout its history.
Hezekiah takes the throne when he is 25 and rules for 29 years. He puts into place some major religious reforms. According to 2 Chronicles 29, once he takes the throne, he has the priests consecrate themselves. King Ahaz had removed the bronze altar from the temple during his reign and the priests put it back where it should be. In the next chapter, he decides to celebrate the Passover. However, all the priests could not be consecrated in time so they celebrate it a little late. Hezekiah invites his entire kingdom and has a great turn out, including some people from the Northern Kingdom. He doesn't stop there. He removes the high places, which were places on hills where the people would go to worship. Many of the "good" kings of Judah had failed to do this. He also destroys the Bronze Snake of Moses because people had been worshipping it.
During Hezekiah's fourth year, the king of Assyria sweeps the kingdom of Israel off the face of the earth, a judgment from God for their continual idol worship. Ten years later, the newest king of Assyria, Sennacherib, attacks Judah an lays siege to Jerusalem. Hezekiah gives him a bunch of gold and silver but that doesn't appease the king. So, Hezekiah cries out to God who sends an angel to smite the camp of the Assyrians and they leave. Hezekiah correctly gives all the credit to God for defeating this mighty army.
Soon after this, Hezekiah becomes gravely ill and the prophet Isaiah comes to tell him that he is going to die. Hezekiah's prayer is simple: Remember, Lord, how I have walked before you faithfully and with wholehearted devotion and have done what is good in your eyes. God changes his mind and grants Hezekiah 15 more years. He also gives Hezekiah a sign and makes the shadows on the stairway of Ahaz go backward 10 places (it was basically a giant sundial, so a sundial's shadow went backward).
Hezekiah's one moment of weakness was when he shows envoys from Babylon all the riches of his palace. Isaiah chastises him for this and tells him that all of his riches will be carried off, along with some of his people.
As I said, Judah's line of kings is a mixed bag and Hezekiah's son Manasseh is perhaps the evilest king of Judah. But that's another story.