I understand what occurs on a regular Li-ion battery - the positive Lithium ion moves from one electrode to the other of the battery. But what is exactly the physical mechanism for this intercalation to occur? Is it that the Lithium in the LiCoO2 electrode lowers the chemical potential between electrodes? I am really curious about the process - any reference would also be helpful!
Yes, lithium ion batteries works with the principle of intercalation and deintercalation of ions from cathode to anode and anode to cathode respectively. To be specific for intercalation, lithium (in cathode) having high oxidation potential oxidize, loosing an electron which goes to the current collector to anode. So lithium ion get positive charge. Since the battery source you use also has positive terminal hence repulsion between ion and positive terminal occurs. Thus positive ion of lithium goes towards anode, which has layered structure thus result in intercalation. Another way of seeing it is because of difference in the concentration the diffusion of ions occur or you can also consider the fact charge neutrality.
Can you be more specific which step you don't understand?
In principle, the main cause for the discharge of batteries is a electrolyte (in the considered case this is some Li salt, usually dissolved in organic solvent), which provides a conductive path for the cations to propagate. A very simple animation and explanation of this process you can see for example here, but I suppose you are already familiar with this.