The blue lightsaber used by Rey was not her own. It once belonged to Anakin Skywalker, who turned to the Dark side and lost his blue lightsaber during his fight against Obi-Wan. Obi-Wan gave it to Luke Skywalker many years later, who also lost it against Darth Vader, and Rey got her hands on it one generation later.

The blue lightsaber was used by three Skywalkers of three different generations. So it is also called Skywalker lightsaber.

Rey buried the lightsaber to honor both her teachers, Leia and Luke Skywalker. She also buried the lightsabers to honor the end of the Skywalker legacy.

Rey was holding a yellow blade Standard lightsaber while she buried the blue lightsabers of the twin Skywalkers. Her yellow lightsaber might represent her connection with both Jedis and Sith lords, but it also meant a new beginning of yet another story in the S-T Wars Galaxy.