A big motivating factor for a withdraw, at least in the propaganda message, was to gain the ability to regulate immigration into the UK. There is a sentiment, accurate or otherwise, that immigrants from other EU countries are straining the UK's economic system, and/or straining the public benefits system. In general, one would surmise that the UK is hoping to preserve as much of the rest of the existing relationship dynamics with the other EU countries, while saving the money the pay to the EU (which is not insignificant), and gaining the ability to better control their borders.
Of course, that's not in the EU's interest, which they were quick to make clear after a meeting. To wit, they said:
"Any agreement, which will be concluded with the UK as a third country, will have to be based on a balance of rights and obligations. Access to the single market requires acceptance of all four freedoms."The "four freedoms" which they note are the freedom of movement of goods, workers, services and capital.
The thing is, while this is meant to be an opening salvo in the negotiations with the UK in a post-EU sense, it's actually not all that bad in a literal sense. I don't think the UK would have much issue with freedom of movement for workers, in the sense of citizens of the EU which are participating in the economy... that seems an entirely reasonable compromise, if they can restrict the movement of non-workers (ie: refugees, and/or persons intent to take advantage of the social services without contributing to the economy).
Of course, that won't be the way the EU will see it, in all likelihood, so it will be a more contentious negotiation. It will be interesting to see how it turns out; I don't think the relationship between the UK and the EU will end up much different than it currently is, but there's a lot of uncertainty there.
Lastly, as sorta an epilogue, I think it's a really good thing that this negotiation might establish some sort of a road map for a relatively bloodless separation of a province from a larger nationalistic organization. There are many instances where that would be very helpful for society in general, and to-date has been a monumentally difficult task for the civilized world. If the outcome of this is something approaching a framework to better establishment of self-governance through voluntary separation from oppressive (or perceived oppressive) regimes, that would be a win for civilization, regardless of the outcome for the UK/EU.