If you do not use closure, you will end up with i being undefined. This is because in each iteration you are overriding what i is. By the time it finishes, it will be undefined. Using a closure will preserve i.
On another note, it's kind of pointless to hard code in values (i.e. i<3) when you can just check for length. This way, if s ever changes, you for loop will still grab everything.
var s = ['john','mark','brian'];
for (var i = 0; i < s.length; i++) {
(function(i) {
setTimeout(function() {
x.innerHTML = s[i];
}, 3000*(i+1));
})(i);
}