We have a new kilogram! The International Bureau of Weights and Measures (IBWM) has retired the international prototype kilogram, an actual piece of metal alloy made in 1879. A better way to define a kilogram was badly needed and as newspaper The Guardian puts it the newly adopted method "instead defines the unit of mass through the electrical force needed to counteract the weight of a kilogram on a machine called a Kibble balance" (link). The underlying fundamental constant for the kilogram from now on is the Planck constant. This constant relates the energy of a photon to its mass (E=hf) and since energy and mass are equivalent is makes sense the the Planck constant has something to say about the definition of mass too.
Max Planck derived what would become his constant in 1894 from the measurements on so-called black body radiation. Any body of mass emits light in a specific wavelength / intensity range and as the temperature of this body increases this range shifts to lower wavelengths. Picture yourself hot melting lava. Planck was the first to fit an equation onto experimental wavelength - intensity plots, an equation with the Planck constant sharing the floor with the speed of light and the Boltzmann constant.
Now we have the electronic kilogram and the Kibble balance. In this device the voltage and current in a wire are measured required to counter the force of a kilogram of mass. A unit of mass can now be measured from the equation m = UI/gv with I (current), U (potential difference), g (the gravitational acceleration constant) and v (an experimental reference). Given a specified mass, the UI product will in turn yield an experimental value for the Planck constant.
But wait, as written up by The Guardian we still need the physical kilogram stored in France to measure the Planck constant, which we can then use to define new kilograms in Kibble machines around the world. But The Guardian misses a point, the IBWM has decided that the Planck constant is no longer measured as 6.626x10(-34) Js but defined as such. It helps that over the years the constant has been measured to a great degree of accuracy and by several methods. It is all in the draft resolutions of the of 26th meeting of the CGPM (link): "the Planck constant (h) is 6.626 070 15 × 10(?34) J s," and "it follows from the new definition of the SI" that "the definition of the kilogram in force since 1889 based upon the mass of the international prototype of the kilogram is abrogated"
(had to look up that one, means abolished)