If you are playing a piece of music in Eb major (3 flats, Bb, Eb, and Ab) and a note was written as Eb is it actually Eb? Or is it D?
It sounds like you're talking about a "courtesy" accidental. If that's the case then it's not strictly needed but is provided as a reminder that the E is flatted and not natural. For instance did the previous measure contain an E natural?
The accidentals in the key signature apply across to all similar letter notes in the staff. In a piece where one of the Key's accidentals is temporarily naturalized in a measure (bar), some transcriptions will place the Key's accidental in the measure also, as a reminder that the note is changed back to what is in the key. It does not stack with the key's accidental.
For example, in Eb Maj if a phrase of the music uses an E-natural, the next measure not using the E-natural may have a flat sign next to the E as a reminder of the switch back. It does not double flat the note to D.