This tests if the window object has a property (filled or not) whose key is "aa".
This operator is very useful because it works even if the value is undefined :
window.aa = undefined; // or just aa=undefined if you're in the global scope
console.log('aa' in window); // logs true
It also works if the property isn't enumerable :
console.log('length' in []); // logs true
In your case, there may not be an aa value, but if the alert shows you true, the property was added to window. 
MDN reference on in
Note that the for...in statement is different in that it doesn't really use the in operator but is a specific construct.
MDN reference on for...in
EDIT : an explanation of your edited question (very different from the first one) :
Your confusion seems to arise from the fact you declared the var aa = 1; in a block. You should know that the scope of a variable in JavaScript is either a function of the global scope and that declarations are hoisted. So your code is in fact equivalent to 
var aa = undefined;
if (!("aa" in window)) { // aa is in window, so we don't enter here
    alert('oh my god');
    aa = 1;  
}  
alert("aa" in window); // yes, the property exists, it's true
alert(aa); // aa is still undefined