Function of solid plane in the NFC antenna
These antennas are from NXP evaluation boards.

These metal parts lower the field-strength output because of the induced eddy currents. They also detune the antenna and the matching network quite a bit.

Without doubt the antenna would perform better without these metal squares, but NXP put them in to show that their NFC solution will work in a real-world NFC device. Typically the antenna is located near a PCB with ground-planes, a display with metal back etc.

They wrote about this design decission in one of their application notes. I think it was the antenna design guide for the PN5180.

If you design your own device based on these antennas you don't have to add these squares even if you don't have a PCB with ground plane near the antenna. In that case consider yourself lucky because you will have a easier time to get good performance out of your NFC.