Rapunzel's Crown is a tiara that belongs to Rapunzel, given to her when she was an infant.
The crown is first seen being given to Corona's new born princess by the King of Corona and when she 'went missing' it became a reminder of her to the Kingdom and it's King and Queen, keeping it safe until their princess returns home.
Eighteen years later it was stolen by Flynn Rider and the Stabbington Brothers for it's gold and diamond value and Flynn took it for himself while he and the brothers were getting away from the guards. When he lost them, the thief found a hidden tower to hide in until the guards and the crazy white horse were gone, but he ended up being hit by a frying pan.
After the girl in the tower, Rapunzel realized that she can take care of herself she found the stolen crown in the 'man's' satchel, she hasn't seen a crown before and it took awhile to find where it is suppose to go; on her head. When Rapunzel failed to get "mother" to say "yes you can leave and see the floating lights in person" again, she made a deal with the thief. She'll give him back his "satchel" if he takes her to the lanterns and brings her back home unharmed. Not long after they left, Gothel came back to the tower to find her "flower" missing; and the sun shining it's light one of the crown's jewels is how she found it and a Wanted Poster of the thief.
Gothel later uses it to get the Stabbington Brothers to help her get Rapunzel back and get rid of Flynn; and she uses it again on Rapunzel as she made her believe that Flynn only cares about the crown's jewels and not her. After Gothel left Rapunzel started to wonder if she really could trust Flynn and that he would stay or leave her once she hands it back to him? The next night when Rapunzel's dream of seeing the flowing lanterns in person finally came true and was about to sent her own up with Flynn/Eugene, she gave the tiara back to him and told him that she was no longer scared of him, but Eugene put it aside. The crown's value no longer means anything to him; only she matters.
Eugene later gave the crown to the Stabbington Brothers, so they would leave him and Rapunzel alone, but they knocked him out, tied his hands and the crown onto a small ship's helm and send them both to the castle. The brothers later went up to Rapunzel and made her believe that Flynn told them about her hair so they would let him keep the crown for himself: Gothel knocks the brothers out before they could grab her. Her plan to make Rapunzel believe that greed for the crown's jewels is more powerful than love worked as she brought her flower back to the tower, while the royal guards got the crown back and locked Eugene and the brothers up for stealing it.
At the tower Rapunzel was having flashbacks of her birth family, seeing a picture of her infant self and seeing herself as a princess in the mirror while wearing the crown; she realized that the crown was hers and that she was the Lost Princess (and that Eugene choosing the crown over her was a lie). Later it was placed back on her head after Eugene had escaped, saved and brought her back home to her real family. But from time to time Eugene still uses his thieving 'Rider' skills on it to tease Princess Rapunzel.
Rapunzel wears the crown with her wedding dress as she and Eugene become husband and wife: and the diamonds on her wedding ring resemble and shine like the tear shape diamonds on the crown.