MODES:
A - is all screen mode. All the screen of transaction are displayed.
N - is no screen mode no Screen is displayed when you executed the transaction.
E - is error screen Only those Screen are displayed where in you have error record.
UPDATES :
S - is for Synchronous updates in which if we change data of one table then all the related tables get updated and them SY-SUBRC is returned i.e., SY-SUBRC is returned for once and all.
A - is for asynchronomous update when we change data of one table, the Sy-subrc is returned. And then updation of other affected tables takes a place so if system fails to update other tables still sy-subrc returned is O.