In its most basic form, a one-state solution to the Israel-Palestine Conflict would produce a single political entity, combining the populations of both the current Occupied Territories and of Israel. It assumes that an appropriate means of representation can be developed, but it rather quickly runs into the challenges of demographics and identities. If the model is democracy, the state model will have to make compromises with respect to Zionist ideals, just as it cannot accept an Islamist model.
This differs from a zero-state solution, in which the Palestinians are returned to Jordanian and Egyptian citizenship and there is no remaining concept of a Palestinian state.
Geographically, the resulting entity would correspond roughly to the original British Mandate of Palestine, with the probable ceding of Gaza from Egypt. The status of the Golan Heights would be an open issue.
One possible parallel is South Africa, which did move to a more heterogeneous model, but only a small number of the previously dominant group believed they had a religious and identity commitment to a particular system. Kuwait and Iraq have been slowly moving to less theocratic models, but the case here is closer to that of Saudi Arabia, where the legitimacy of the government is tied closely to its relationship to specific religious matters; the King's most important title is Guardian of the Two Holy Places (i.e., Mecca and Medina).
A very critical issue is the status of Jerusalem, holy to Jews, Christians and Muslims. Indeed, the general position of Israel is that it must control Jerusalem as a whole, while many Palestinians see East Jerusalem as the logical capital of a Palestinian state.
While the UN General Assembly recommended the creation of Israel as a Jewish state, some regard two-state as a violation of the Universal Declaration of Human Rights, as it discriminates by religion. Of course, this is very much the case in Saudi Arabia and many other Arab states.