Struggling to find a good definiton for Gabor-Descriptor
In this context, $j$ is the imaginary unit: $j = \sqrt{-1}$. The complex exponential function represents what they call an "oriented sinusoidal grating." The fact that $j$ is the imaginary unit in this case can be verified by noticing the relationship between $(1)$ and $(2)$ in Section 2; this is an example of the frequency-shifting property of the Fourier transform. That is, multiplying the Gaussian function $h(x,y)$ by the complex exponential function results in a shift in the Fourier transform of the result along the axis that the sinusoid runs across (the $x$ axis in your example).