In 1947 the UN General Assembly voted to partition what was then the British Mandate of Palestine into a Jewish and an Arab state. As a result Israel came into being. The Arabs rejected the decision and no Arab state was created.
In late 2012 the General Assembly voted that "Palestine" be granted non-member observer status. Why didn't they create a member state?
Basically the only body in the UN that can take any binding decisions is the Security Council and the five permanent members can veto any decisions they don't like. The other ten members are taken in turn from the various regions. As members of the council they can put things on the agenda for discussion.
In 2011 Lebanon was briefly chair of the council and proposed that the council accept the Palestinians as a state. The Security Council referred the issue to its membership committee for investigation and the membership committee came back with inconclusive results since the Palestinians failed to meet some of the conditions of the UN charter. The committee recommended an intermediate step of granting the Palestinians observer status by the General Assembly, which apparently is the most the General Assembly can do without Security Council backing. The issue was thus not presented to the Security Council, but maybe at a later date. The point of this decision was, I suppose, to prevent international conflict over the issue by deferring it.
Back in 1947, the Security Council decided it couldn't be bothered with the whole Palestine thing and handed the issue over to the General Assembly. That's why Israel was created by the General Assembly. The 1947 General Assembly decision called on the UN take various actions which the Security Council refused to take, so no one actually worked to implement the decision and the new state of Israel was forced to fight for its existence, it was eventually admitted to the UN in March 1949, following a Security Council decision:
"The Security Council, Having received and considered the application of
Israel for membership in the United Nations, Decides in its judgement that Israel is a peace-loving State and is able and willing to carry out the obligations contained in the Charter, and accordingly, Recommends to the General Assembly that it admit Israel to membership in the United Nations,
Adopted at the 414th meeting by 9 votes to I (Egypt), with I abstention (United Kingdom
of Great Britain and Northern Ireland)."
In those days, there were less council members and US television companies broadcast UN Security Council discussions live.
Had the Security Council decided in 2012, to accept the Palestinians into the UN, the USA would almost certainly have vetoed the decision. Vetoing decisions is embarrassing for the permanent members of the Security Council and implies they lack moral authority. That is really the most the Palestinians can aim for, but as it was no veto was required. While this is a bit of a failure for the Palestinians, the issue is still out there and has simply been deferred for the time being.
The Israeli press have widely quoted the Palestinians as saying they will use their new observer status to take issues to UN's International Court of Justice (at the Hague: homepage), however they may find that it makes awkward decisions for them too and even if it decides in their favor, all the court can do is make a recommendation to the Security Council on legal matters.