In its most basic form, a two-state solution to the Israel-Palestine Conflict would produce two independent neighboring entities, one Palestinian and one Israeli. To some extent, this reflects the original geography at the time of the United Nations resolution that partitioned the 1922 British mandate of Palestine into Israel and Transjordan.
At this point, there are an enormous number of details that would have to be resolved, many of which having solutions that are acceptable to some interest groups and anathema to others. One major issue has been called "land for peace". The current borders of Israel and the Palestinian territories do not follow the partition lines, but the ceasefire lines after the 1967 Arab-Israeli War. Many proposals suggest changing the lines to reflect boundaries that make better sense for economics, security, and ethnicity. Obviously, this would force some relocations. United Nations Security Council Resolution 242 framed the position in terms of withdrawal back to the lines of partition, but with a guarantee of peace.
A very critical issue is the status of Jerusalem, holy to Jews, Christians and Muslims. 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 created 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.