King Henry IV is gravely ill, mostly because he's worn out by the civil rebellion that's plagued his reign and also because he's spent so much time worrying about his wild child son, Prince Hal, who is heir to the throne. Prince John squashes the rebel uprising in a surprisingly easy and anticlimactic moment but, King Henry faints when he hears the news of Prince John's victory. Plus, he's still at odds with Hal.
Prince Hal rushes home to his father's bedside, where he watches sadly as his ailing father sleeps. Thinking dear old dad has gone to heaven, Hal makes off with the crown. Then, surprise! King Henry wakes up and goes off on his rotten, good for nothing son. Hal explains that his dad's got it all wrong – he loves his father and promises to be a good king when Henry does die, which is going to happen sooner rather than later. All is forgiven and then…Henry dies.
Now that King Henry's dead, everyone stresses about what kind of King Hal will be. Is he going to run the kingdom into the ground? It turns out there's nothing to worry about because Hal embraces the Lord Chief Justice as a trusted advisor and a "father" figure who will guide him as he rules England. When Falstaff shows up to celebrate Hal's coronation, the newly crowned King Henry V publicly banishes him, showing once and for all that Hal is not messing around. Hal is taking this whole king thing very seriously, starting with his plans to wage war against France, which we can read all about in the play's sequel, Henry V.