You're not wrong, but rather than thinking of possible worlds as being "inside" other possible worlds, it's better to think of some worlds as being possible relative to others.
For example, let's say it's possible to fly to the moon. That means that there is a world - call it v - which is possible relative to our world, in which we do fly to the moon.
But there might be another possible world - call it w - where we have used up all the fuel, and so it is not possible to fly to the moon. In this case, v is not possible relative to w.
According to possible worlds semantics, A is true at a possible world w if and only if A is true at every world v which is possible relative to w.
So A is true at w if and only if for every world v possible relative to w, and every world u possible relative to v, A is true at u.
Likewise <>A is true at w if and only if at some world v possible relative to w, A is true at v. So <>A is true at w if and only if at every world v possible relative to w, there is some world u such that A is true at u.
One reason for your confusion might be that in one of the simplest modal logics, S5, every world is considered possible relative to every other.
In this case if A or <>A are true at any world, they are true at every world, and so A and <>A end up saying much the same thing.
But in other modal logics in which not every world is considered to be possible relative to others, more interesting things can happen.