How do comment replies work?
In Twitter the at (@) symbol makes the tweet appear in the user page.
Does it do anything on Stack Overflow?
It does not do anything as far as programming. It is just a social construct we have all adopted to show who we are addressing our comment at.
And now, it also notifies the target:
I would back the idea of having the @[USERNAME] actually try to predict the user being addressed and place a link to their profile. Overall though, @TheTXI is correct, it is becoming a social construct (thanks to twitter) that we are beginning to adopt and adapt into other tools.