In Apple's definition, a combination of EQ, phase and time delay, along with a totally different mix than either the multichannel mix or the normal 2 channel mix. I suspect that vocal frequencies are matrixed to make it possible to process them separately from the rest.
In Boom, the "Spatialize" control adds reverb delay, "3D" adds phase processing, and "Fidelity" seems to do what "Sound Enhancer" does in iTunes. I think that is called an "Exciter"? Not sure about that though. All three of those can be dialed up or down. Boom also has a ten band graphic equalizer, night mode (which is a compressor), pitch adjustment up and down, and "ambience" which I can't discern doing anything at all.
That's the best I've been able to figure it out based on listening to a bunch of stuff. Dolby and Apple are tight lipped when it comes to details about what Spatial Audio is and how it works. They just describe it with sales pitch and avoid technical explanations. There's a certain amount of emperor's new clothes involved. Playing with the settings in Boom has taught me some of what the different elements of the processing in Spatial Audio do. Boom can get really close to what Spatial Audio does, but not limited to Apple approved sources. In fact, it it was possible to get the track Apple uses for Spatial Audio, I bet you could exactly match it with Boom 3D.