Just move it in Object Mode (Tab to toggle)
The Mirror modifier works according to the Origin (aka pivot) of the object - that is the orange dot that shows on selected objects - unless you specifically tell it to use a different location (by selecting something for the Mirror Object)

In Edit mode, you are manipulating the vertices/edges/faces of the mesh itself, not the object as a whole, so when you select everything in edit mode and move it about, the origin stays where it was and thus the mirrored mesh goes out of alignment:

So instead, Tab out of edit mode and move the entire object.
If you wish to reposition the origin of the object without moving the mesh, you can use Shift+S to place the 3D Cursor at some position, and then Ctrl+Shift+Alt+C in object mode to move the origin to the 3D cursor.

You may notice the Origin to Selected button in that screenshot, this is not a built-in function of blender but rather a function in my own addon that simply performs these two functions in one go since I do this frequently. If anyone is interested, I could upload this addon.