The king's exhausted from civil war (a problem his rebellion and deposition of King Richard II helped create). Henry wants to redeem himself from his past sins by waging a Holy War. This, he hopes, will also help smooth the way for his eldest son, Prince Hal, who will inherit the throne.
The rumble in the Holy Land is put on hold because Henry's got problems at England's borders. One thousand troops have been slaughtered by the Welsh, who have also captured Mortimer. There's also been a battle at Holmedon with Scottish invaders. The English have defeated the Scots, but Young Harry Percy (Hotspur), an English nobleman, refuses to give the king his war prisoners. Meanwhile, Prince Hal is spending all his time drinking, stealing, and carousing with common criminals. No wonder Henry's so tired.
After an unproductive meeting with the king, the Percys (who feel slighted by the man they previously helped to the throne) plan a rebellion based on the claim that Mortimer is the legitimate heir, not Henry. At the same time, Prince Hal and his loser pals plan a highway robbery and hold up the king's exchequer (treasury) at Gads Hill. (Notice a parallel here? Everyone's being naughty.) But, Hal shocks the audience by claiming he's just pretending to be a bad kid so he can stage a glorious "reformation" that will amaze everyone.
Things take a major turn when Prince Hal redeems himself on the battlefield. Not only does the prince save his father's life, but he also defeats the valiant Hotspur, quashing the rebel's hopes and confirming that he, Prince Hal, is fit to one day rule the country.
After playing dead so Douglas won't kill him in battle, Falstaff heaves himself off the ground and spots Hotspur's corpse. Falstaff stabs the dead body (just in case Hotspur's faking his death too) and hauls the carcass off like a trophy. Hal lets him get away with the pathetic gesture, which seems like a sign of the prince's new maturity.
Because Douglas has demonstrated courage on the battlefield, Hal makes the executive decision to let him go free without ransom. According to Hal, it's the honorable thing to do. Vernon and Worcester, however, are not so lucky. There's a sense of poetic justice here since these are the guys who decided not to tell Hotspur about the king's offer of peace prior to the battle.
King Henry dusts his hands off and congratulates his men for a job well done. But, there's more to do. Henry decides that he and Hal will ride to Wales to duke it out with Glendower and Mortimer, while Prince John goes to York to mop the floor with Northumberland (Hotspur's lame father, who called in sick to work to avoid the battle at Shrewsbury). The story continues in Henry IV Part 2.