The mirror modifier mirrors according to the origin point, it just so happens that your origin point is at the world center. You can move your object in edit mode if you want to leave the origin point stationary. You can also go to the Options menu and toggle Origins, that way you can move your object’s origin point and your mirrored side will follow along.

Alternatively you can use an empty or any other object as the designated center with the Mirror Object option in the modifier.
