The "3D" part of that description refers to the fact that, like Dolby Atmos, DTS:X adds a height or overhead effect to the surround sound experience to create a more realistic sense of immersion. For instance, if a plane flies overhead in the film soundtrack, a DTS:X setup with overhead speakers allows that sound to be precisely located above you, instead of being forced off to the sides.
The "object-based audio" description refers to a completely different way of mixing the audio. Instead of being limited to a certain number of channels, object-based formats allow the sound mixer more freedom to place audio elements around the soundfield, and it gives end users more freedom to build a surround sound system to replicate that experience.
DTS says that DTS:X is more flexible than Atmos, which depends on the use of a few specific speaker layouts. DTS:X allows commercial and home theater designers to put speakers almost anywhere within reason, and the system will "map" the correct sounds into each speaker. In the home, the system supports up to 32 speakers. You can read more about the technology here.
DTS first announced DTS:X for both the theater and the home in December 2014; in the spring of 2015, the company provided a more detailed plan of how the format would roll out in theaters and in the home.
To enjoy the DTS:X experience, you will need an AV processor that can decode DTS:X, a Blu-ray disc that includes a DTS:X soundtrack, and the extra speakers necessary to create the overhead effects. DTS:X does not embrace the up-firing speaker approach that Dolby supports for Atmos, where the height effects can be reflected off the ceiling so that you don't have to install in-ceiling speakers.
The majority of AV electronics manufacturers now include support for DTS:X in their newest mid- to high-end AV receivers and processors. However, as of March 2016, most of those products are still just "DTS:X ready," meaning that they are awaiting a firmware update to officially add the technology. Denon and Marantz are the first companies to actually activate DTS:X in their products.
On the software side, the first crop of Blu-ray discs to include a DTS:X soundtrack have also arrived, and you can view the list here.
• Can DTS:X Get Off the Ground?
• Denon to Add DTS:X to Top-Shelf AV Receivers
• DTS:X Coming Soon to Top-Shelf Marantz AV Receivers and Preamps
• Yamaha Announces Timing for DTS:X Upgrades