What is it? The answer is energy.
How can energy have mass? Einstein actually answered this question with his famous equation, E=mc2. Every bit of energy has an equivalent measure in mass. Faster moving particles are actually heavier due to their higher inertia, and photons even carry a tiny bit of mass. The sun emits 5 million tons of photons every second!
So how do we know how much global civilization uses? Wikipedia has a good article summing up the energy use of the world. In 2015, we used 500 exajoules of energy. Since energy translates to mass at a rate of 90 petajoules per kilogram, that translates to about 7 tons.
See also:
Orders of Magnitude (Energy)