I'm aware that ions conduct electricity, however, most of the sources I've seen give me only a really basic explanation of why this happens. Does anyone have a really in-depth way of explaining this?
Ionic solutions (electrolytes) are 2nd type conductors, i.e. their electric conductivity is connected with a mass transfer. In electric fields their anions move to a positively charged electrode and there donate electrons to be electroneutral whereas their cations move to a negatively charged electrode and there accept electrons to be electroneutral as well.