Boom-Boxes are items that can be obtained once per day. The contents of Boom-Boxes are randomly generated and can range from anything like Mounts and Mount Customization Sets, to Costumes, Dyes, or Crafting Materials.
Boom-Boxes can now only be obtained by playing on the Wildstar test server (PTR) when Carbine is requesting for assistance in testing a new feature. They will announce what days are eligible to be earning Boom-Boxes on their forums and what activity they would like you to participate in (Examples: Daggerstone Pass, Blighthaven Quests). Unfortunately there is no set days where you can earn Boom-Boxes, it is based entirely off of Carbine's announcements.
In regards to Deluxe Owners getting Boom-Boxes, I believe they are referring to that if you pre-order you got access to the beta, which gave you 3 Boom-Boxes per day of logging on.