The hub is a CPU with radio antennas.
The DTH is software, a device driver. Most of these run in the cloud, a few of them can run locally on the hub itself. But what happens is when the hub wants to use one of those radio antennas to communicate with a specific device, like the GE module, The request gets run through the DTH so that it will be formatted into the exact string that the end device expects. And the same thing coming back the other way. The end device sends a radio signal to the antenna in the hub, it is received and run through the device type handler to be translated into something that the smartapp software on the hub or in the cloud can understand.
The communications between the hub antenna and the end device are always the same, but different device type handlers may interpret them differently. A good example is that some devices allow for a tap, double tap, or long hold on a switch. The device type handler typically converts those to look like button one, button two, and button three, and then reports those “events” to whatever smartapp has been subscribing to that switch. That way One smart app can process events from many different devices, with many different form factors, because the device type handlers convert the actual events into this common structure. 
You’ve probably already seen the custom code FAQ, but if not, you’ll need it to be able to use the tweaker anyway, so here it is. It covers the main concepts.