The minimized mode is currently abandoned option. To use it you have to select the option "Old Style Interface" in the Main settings tab. Note that this option is not compatible with Windows 10.
When APT is minimized small floating window will become visible, you can drag and place where it is comfortable with you. In this floating window the same messages will be shown as in the status monitor in the main APT screen. This allows seeing what is the APT status during you use your guiding or other tools. Also you can see the number of the taken images and the total number in the current plan. If you want to restore APT window, double click with the left mouse button on the floating window, or use right mouse button over the APT icon in task bar and select “Restore”
The status window will be expanded automatically when the preview option in the main the Camera Tab is ON and will display the center of the image in the main window. With right mouse button click you can hide/show the small preview area.