Rory's bracelet is a present from Dean for her 16th birthday.
It becomes a symbol of their relationship, and Dean gets very upset one day when Rory is not wearing it. Rory had lost the bracelet (but did not notice until Dean points out it is missing) while having a picnic with Jess. Jess finds it and picks it up, but makes no mention of it to Rory. Lorelai, seeing Rory upset about Deans reaction to the missing bracelet, finds out that Jess has it and confronts him about it. After Dean breaks up with Rory at the dance marathon, she doesn't take it off, but it symbolically breaks in the shower.