Many classic comedies begin by showing us a "villain" character: the jerko who creates a lot of unhappiness for the other characters, and especially for the hero. Harpagon is our Villain-with-a-capital-V. Harpagon is an overbearing miser and makes life miserable for his son, daughter, and servants.
His son Cléante wants to marry a beautiful young woman named Mariane, but it turns out that the greedy d-bag Harpagon wants her for himself. Ol' H wants to marry his daughter off to a rich old man named Anselme, but his daughter Élise really wants to marry one of her Daddy's servants, Valére. It's pretty clear in this early stage that the main obstacle to everyone's happiness is Harpagon and his bottomless greed.
The forces of frustration that present themselves to us at the start of the play only get worse as the play gets going. Élise tells her Daddy-o that she doesn't want to marry Anselme, but Harpagon commands her to do so. Cléante reveals his love for Mariane, but Harpagon nixes their union because he wants Mariane all to himself.
While all of this is happening, Harpagon's casket of buried money goes missing from the yard where he buried it (like a freak), and the dude throws an absolute hissy fit. He gets a police officer and vows to hang whoever stole his money. Valère seems to admit to the crime at first, but it turns out that he's just admitting to having a super-crush on Harpagon's baby girl. Harpagon remains committed to ensuring that everyone around him remains as miserable as possible. He's also committed to getting his money back.
The Revelation Stage
Like in most classic comedies, The Miser ends with a big ol' revelation that changes the lives of every character in the play. It turns out that Anselme, the older wealthy man who's supposed to marry Élise, is both Mariane and Valère's father. Ta-da!
Because he's a great guy and wants his kids to be happy (unlike a certain villain whose name begins with an H and ends with an N), Anselme uses his money to buy out Harpagon. He makes sure that Cléante gets to marry his daughter Mariane and Élise gets to marry his son Valère.
You comedy lovers out there might be thinking, "Hey, doesn't the villain usually go through a change of heart at the end of a comedy?" The keyword there is 'usually,' folks. Molière was a cynic, skeptical of people's abilities to change their deepest flaws. So at the end of this play, Harpagon remains the same bitter old miser he's always been. Heck, it even sounds like he's going to get his money back.
But on the bright side, at least Harpagon no longer has the power to make his son and daughter miserable. Now he's left alone with only his servants to abuse.