What's an Air Gap Layer in a PCB?
As Peter Bennett said, the air gap layer is probably a Gerber containing areas to be milled out of the layers, possibly the top and bottom prepreg, leaving the core intact. Since there are only 4 copper layers, this would likely leave open cavities on the top and bottom with copper potentially exposed on the power/ground layers. 

This could be used to recess components into the PCB. 

In some cases, components are completely embedded into the PCB. 

I believe this process typically would have the (in this case) core run through a pick and place machine, soldered, cleaned and then laminated and the holes plated through with the top and bottom prepreg. 

Here is an example of a stackup with completely embedded components from Altium: