The question
The light cone
Why does light leaving you make a sphere, and what is inside it?
The moment you were born, light left the Earth carrying an image of it. It has not stopped. This is what that sphere actually is, and what it does and does not mean.
Nothing carries the picture — the picture is the light
It is tempting to imagine a signal being sent, as though the Earth broadcast something at the moment of your birth. Nothing was sent. Light was already leaving, constantly, as it does from any lit object, and some of it happened to leave at that instant. What makes that instant yours is only that you started then.
So the sphere is not a message. It is a boundary. It marks the furthest distance any information about that moment could possibly have reached, because nothing carrying information goes faster than light. Everything inside the sphere could in principle have learnt about your birth. Everything outside it could not — not yet, not by any means at all.
Why a light-year is a distance and not a duration
A light-year is how far light goes in a year: about nine and a half trillion kilometres. That makes the arithmetic of this tool almost embarrassingly simple. Your light has been travelling for as many years as you have been alive, so the radius of your sphere in light-years is your age in years. The number the counter shows is, quite literally, how old you are.
This is why the two readings on the tool are the same measurement twice. The radius in light-years is your age; the distance in kilometres is that age multiplied by the size of a light-year. Nothing else is going on.
What it means that a star is inside the sphere
When the tool says your light has reached Sirius, it means the light that left Earth at your birth has now travelled the 8.6 light-years to that star. It does not mean anyone there has seen anything. There is no one there. And even if there were, what arrives is not a picture of your birth in any useful sense: light from the whole Earth, of that entire instant, spread thinner and thinner across an ever-larger sphere until it is immeasurably faint.
The honest statement is about possibility, not observation. A star inside your sphere is a place where news of your birth could have arrived. That is a smaller claim than it first sounds, and a stranger one: it means the universe is divided, from your point of view, into the part that could know and the part that cannot.
Why it can never be called back
The sphere only grows. There is no mechanism that shrinks it, because that would require information to travel backwards in time. Whatever left, left.
This is the part people find sticks with them. Not that the number is large, but that it is one-way. Every second you spend reading this, the boundary of what could know about your beginning moves another three hundred thousand kilometres further out, and none of it comes back.
What the drawing is not
The plate in the tool places each star at its true distance from the Sun, but sets the angle by right ascension alone. That is a flattening: real stars sit in three dimensions, and two stars drawn next to each other on the plate may be nowhere near each other in space.
The distances are honest and the sphere is honest. The arrangement around the circle is a convention for fitting them on a page. We would rather say so than let a picture imply a precision it does not have.