Same Origin Policy(SOP) is often mentioned together with Cross Site Scripting(XSS). But it seems that in the world with SOP, XSS still happens from time to time. So I am never clear about what exactly kind of attacks do Same Origin Policy prevent? In other words, imagine a world without SOP, what other power a malicious attacker could gain compared to the real world with SOP?
I read on this website(http://security.stackexchange.com/questions/8264/why-is-the-same-origin-policy-so-important) that "Assume you are logged into Facebook and visit a malicious website in another browser tab. Without the same origin policy JavaScript on that website could do anything to your Facebook account that you are allowed to do.". This actually makes me even more confused because I have never heard of any mechanism for webpage in one tab manipulating other tabs even from the same domain. It is also mentioned (more explicitly) here (http://javascript.info/tutorial/same-origin-security-policy) that SOP prevents script in one window to manipulate DOM elements in another window. But I really cannot relate the example to what is explained (what does window mean here? it seems that the example is talking about iframe).
To sum up, can anyone give some concrete examples of what can happen if there were no SOP?
Also, I am curious about how script in one window can manipulate DOM elements in another window assuming the two window are from the same domain. But this is not the main course of this question
Thank you!