The move tool does not work. The selected object stays the same

Thank you so much for your answers and suggestions. I am new to photoshop, so it takes a while to figure it out that I did not select the right layer.

Are you sure you are using the Move tool? When you drag your mouse on an image with the Move tool, the selected Layer moves.

If you have a selection, bounded by marching ants, and you drag your mouse with one of the Selection tools, you will move the selection and not the contents of the selection, and will see the coordinates—which sounds like what you are describing.

If doesn't fix the issue, please share a screen shot that includes the Tools bar and the Layers panel so that we can see what is happening,

After making the selection of the object on the layer, hold down the Cmd key and drag the selected area. Move tool is not involved.

If, for some reason, you want to use the Move tool, after making the selection, choose Edit > Copy and then use the Move tool.