So the topic of what is a cold migration (in VMware vMotion speak) came up in a conference call today with a customer.

It is a migration strategy when there are CPU compatibility constraints between certain revisions of CPUs, it basically means there is no path to use v-Motion as such so will associated outages.
When does it occur?

As mentioned, cold migration is a strategy or a decision to migrate virtual machines between different revisions of CPU (whether it be manufacturer or models). An example might be going from an AMD chipset to an Intel chip.  There are cases that going from the same vendor CPU requires an outage so cold migration would be an option.  More information on what to check, how to check can be found here

What happens? 

Quite simply, the virtual machine is powered off on the source host and powered on, so there is an outage but as long as both ESXi servers have visibility to the same shared storage, then cold migration can be very fast and the virtual machine downtime kept to a minimum.
The difference to vMotion

The biggest difference, vMotion is (typically) performed without any downtime on the virtual machine whereas cold migration requires an outage to power down and power up the virtual machine on the destination host.

Another notable difference it happens at a management network layer and not the VMKernel layer (which vMotion uses)

That is cold migration in a nutshell!