This equation describes the "skin depth"1 (`d`) of an electromagnetic wave in a conducting medium. The "skin depth" is how far the wave can travel before the amplitude of its electric field is reduced by a factor of `1/e`
A graph of the electric field amplitude as it propagates
In the picture, the independent variable is `x/d`, or how many multiples of the skin depth the wave has traveled. The dependent variable is the ratio of the current Electric Field Amplitude, `E(x)`, to the original Electric Field Amplitude, `E_0`. After the wave has propagated one skin depth into the conductor `(x/d = 1)`, then the ratio `( E(x) )/ E_0 = 1/e`, i.e. `E(x) = E_0 / e`.
For more information on `tilde k` and how it's use, please refer to EM waves (attenuating) in a conductor.