Suppose there are only three people with blue eyes. A knows that B can see at least one blue-eyed person. And B knows that C can see at least one blue-eyed person. But A doesn't know that B knows that. A reasons: if I have brown eyes, B can only see one blue-eyed person, ie C. And if B can only see one blue-eyed person, he will reason "if I have brown eyes, C cannot see anybody with blue eyes". Thus, if I have brown eyes, B does not know whether C can see anybody with blue eyes.
Or when there are four blue-eyed people, A's reasoning will be: if I have brown eyes, then B will only be able to see two blue-eyed people. He will then reason according to the above case. So if I have brown eyes, B doesn't know that C knows that D can see at least one blue-eyed person.
By saying "I see a blue-eyed person", the foreigner removes this uncertainty.