Each SPIP user can modify his own display (without affecting the display for the other users, contrary to the «Precise configuration» page).
Several SPIP features are very rarely used (or not at all) by some editors. Therefore, choosing the «simplified interface» allows to lighten this interface and to simplify its comprehension. In this mode, only the elements really necessary to the management of the site are displayed. For example, very few users need the «date of earlier publication» which does not appear in the «simplified interface» mode.
P.S. the differences between the two mode of display are more obvious to the administrators who have at their disposal more features than the editors of the site.