The mirror modifier uses the object’s origin point (the yellow dot that appears when you select your object) as the point from where to start mirroring from. If you move your object in object mode, the origin point will come along and the mirrored side will come with it. If you move your object in edit mode, the origin point doesn’t come along and the mirrored side will act accordingly, or in other words, the moving in the opposite way behavior like you were expecting. The gizmo will be displayed wherever your origin point is.
If you want to watch the full list of modifiers explained, you can watch the Modify course:
https://cgcookie.com/lessons/lesson-8-mirror-modifier
