You can specify exactly how Emacs reminds you of an appointment, and how far in advance it begins doing so, by setting these variables:
appt-message-warning-timeappt-audiblet (the default), Emacs rings the terminal bell for
appointment reminders.
appt-visiblet (the default), Emacs displays the appointment
message in echo area.
appt-display-mode-linet (the default), Emacs displays the number of minutes
to the appointment on the mode line.
appt-msg-windowt (the default), Emacs displays the appointment
message in another window.
appt-display-duration