The meaning of this sentence is not specific to French language. You can translate it directly and then try to understand by yourself.
It looks like an old badge probably worn by “walkman” users, when such a device was considered as very “high-tech”.

As Gregala wrote, it is probably a badge worn by early Walkman adopters from back when it was considered a high-tech device.

The word “baladeur” was created by the Office québécois de la langue française back in 1989. In France, the Commission générale de terminologie et de néologie accepted the word in 2000. It is a neologism for “Walkman” that comes from the verb “balader,” which means to wander around, to take for a walk, to stroll.

The sentence means: “I wander around with my own ambient music.”