What it does is take ultra-thin chip dies, 120 microns in this case, and stacks them into a single package. The
bottom layer is 10mm on a side, then 9 above it, and 8 above that.

The top layer can also be much thinner, in this case only 50 microns. You can put a fourth die on, possibly more, but in practice, few if any do that, TI uses three.

With the naked eye, it is very hard to see the resulting pyramid shape, you mostly have to look for where the light reflects differently at the edges. These are really thin packages, which is why they tend to get used in cell phones and small cameras.
A typical package is one logic and two flash dice stacked up, basically a complete computer on a slab. The NM-EFD1A will pick up chips that size to 25mm on a side, stick them on a carrier, and hold them in place until the adhesive cures. It then does it again on top of that one with a different die.
One thing to note, this is simply a physical stacking, not electrical. The chips are electrically connected to the outside world with wire bonds not shown here or done by this machine. ยต