Just because there’s a UN Resolution passed, doesn’t mean everything that’s proposed magically happens. Governments of all levels accept long-term plans, but then they need to do further actions to follow through on those plans (or in many cases, they don’t do anything and those plans just stay as dreams and what-ifs).
Israel is a state because they’ve declared it and the UN has accepted Israel as a member, it’s really that simple. If you want to know why Israel’s statehood was accepted, that’s very, very complicated and involves millennia of history. I certainly can’t condense it here, maybe others could, but I doubt it. I honestly think Wikipedia’s a pretty good source for the history of Israel, and I’d suggest starting the British Mandate and looking back if you need more context.