The "Move controls on expand text or list" option works only with text or list controls. If you don't check "Move controls on expand text or list", then the text box or the list box will expand vertically as needed but no other controls will be affected. This could be useful if you have some special window design where the rest of the controls should remain where they are, but obviously this may cause the text to overlap over other controls.
If you tick this option, then all the controls below the bottom line of the text box or the list box will move down, and all the controls surrounding the text box or the list box will resize accordingly, so the window will "stretch" to make the whole text or the whole listbox fit in the report.