Hee Hee.... How did you know that of the few threads I read here, I would be drawn to this one!
Dr. Daniel Siegel has many of those answers. Granted he does not work with Dissociative Disorders, but integration of course happens with everyone. The book the Developing Mind is a gem when it comes to understanding this. Siegel has a lot of free youtube videos on the net, and he sells a great one called the Neurobiology of we, for those that like to listen instead of read. The Trauma and Dissociation wiki has a page in progress on integration. I believe it's awaiting an expert to add and review it, but still what I have read there is pretty solid. A lot of others people have also taken Siegel's teachings and summarized them, which you could find on the net with a search. Just off the top of my head, let's see what I can do to answer this GIANT question!
I know that DID is caused by the personality part of the brains, the neurons don't connect properly, so when you integrate, what happens to the neurons, does anything really change neurologically?
Daniel would tell you that this is the total key to happiness in all humans. All humans need to work on mindful integration throughout life. He explains the 9 domains of integration that all humans should strive for. The final step is Budist-like, and I know most of us will settle for far less that that.
It's important to understand that Memory Integration is a separate process from State integration. They each are one of the 9 steps, that all humans must work on. Of course if you have OSDD (formerly DDNOS) or DID then you have far bigger hurdles, but still it's all the same process.
Daniel's first step is the Integration of Consciousness - which is in the case of those of us that suffered trauma - We are influenced by our past trauma! Without this step of integration we will remain dissociated - fuzzy headed and ill.
His 2nd and 3rd steps talk about mindfully bringing different parts of the brain into the whole process of integration. The particulars are fascinating, but unnecessary to understand. What is necessary is that you must be consciously aware that all of you needs to integrate and invite all of you to do such. Seigel calls this mindfulness.
The 4th step is memory integration. Our early childhood trauma is stored as implicit - only memory. We need to get those little buggers processed through the Hippopotamus so they go to where they need to be and become Explicit memory. This in the case of those with trauma needs to be done with a Therapist. Without trauma memory storage as explicit is a natural and normal process.
The 5th step is Narrative Integration - In this step one will integrate/link to make a narrative story of their life.
Finally the 6th step is State integration, which of course is the integration of alters, or those without alters, the integration of self states. This is not killing off or removing alters, it is linking them together so they have better communication and functionality. As you put forward in your question, you understand that all human personality is made up of parts. In the first few years of life the normal process if for those parts to link/integrate and function well together. If abuse happens, and this normal process is interrupted, then we have to get our head together (pardon the pun) and be smart, and learn how to do this process that is so easily done as a child with proper care.
The 7th, 8th, and 9th steps are important to obtain intimate mental health.
Now beyond Siegel and diving into DID specifically..... looking at the ISSTD 2011 Guidelines
Final Fusion - This is the point where alters will experience themselves as joining together. This is a different process than integration. Kluft reports that this step is important. Those that do not obtain this step are open to regressing and then having Covert (Florid) DID, and PTSD if stressed.
I hope this helps!