FPGA can also be described as programmable hardware.
Programming FPGA is like building a circuit. After downloaded the program to the hardware, the corresponding circuit is built on the hardware. Each input signal will just go through the predefined logic gates and the expected output signal can be obtained.
A very large majority of people wouldn't be able to use or wouldn't have a use for a machine with an integrated FPGA. It would probably be easier and more efficient to get a standalone FPGA if you needed the reprogrammable hardware.
Edit: apparently they do exist: https://www.extremetech.com/extreme/184828-intel-unveils-new-xeon-chip-with-integrated-fpga-touts-20x-performance-boost
A presentation from CMU on how the FPGA on the Xeon chip works here
Companies like Microsoft and Amazon already uses FPGA to speed up SDN process.
Slides from CMU ECE department talk about the combination usage of CPU and FPGA in machine learning area. Xeon+FPGA Platform for the Data Center
FPGAs are becoming common in high frequency trading companies as well. Of those I know of, FPGAs are not their primary method yet, but they are putting effort into using them to speed up their trades.