Peter Quill's Walkman was an object owned by Peter Quill, given to him by his mother as a gift for her fatherless, lonely son. He became very protective of his Walkman, as it was the only thing Peter had left of his mom. It also came with a headset.
However, it was destroyed by Ego in order to break his son. Later, Peter was given a Zune by his former rival and teammate, Kraglin, which Yondu intended to give to his son if Peter's relation with the Guardians didn't work out.