Why are all real frequencies located on the Imaginary axis of the s-plane. I'd like to understand intuitively why this is true?
Take the complex (Laplace transform) variable $s$, and look at the basic exponential signal

$$x(t)=e^{st}\tag{1}$$

With $s=\alpha+j\omega$ we have

$$x(t)=e^{(\alpha+j\omega)t}=e^{\alpha t}e^{j\omega t}=e^{\alpha t}(\cos(\omega t)+j\sin(\omega t))\tag{2}$$

From $(2)$ you see that the real part $\alpha$ takes care of the exponential amplitude, whereas the imaginary part $\omega$ determines the frequency of the signal. If $\alpha=0$ (i.e., $s=j\omega$ is on the imaginary axis) you have an undamped sinusoidal signal with frequency $\omega$.