I know this is a fairly basic question, but can someone explain to me why the harps/horns play in a different key than that of the band? I understand their key is 4 semi-tones higher (e.g., if I am playing in the key of A, they will play in D). Does that really mean when I strike the root note of A, they would be playing a note of D? Thanks.

that's sort of two questions.
as I understand it for harps, it has to do with modal issues relating to the Mixolydian/Dominant scale vs. It's Ionian/Major scale.

" Does that really mean when I strike the root note of A, they would be playing a note of D? Thanks." No

and as I understand it for horns etc., it is strictly for the purpose of writing instruments parts within reasonable boundaries of the staff.

the range of 'Eb' instruments fit 'better'(more within the staff lines) in the staff if you pretend (or transpose) that what really is a C is an Eb, or vice-versa.

someone else can probably explain more clearly. Especially the harp thing...

...and as I understand it for horns etc., it is strictly for the purpose of writing instruments parts within reasonable boundaries of the staff.

the range of 'Eb' instruments fit 'better'(more within the staff lines) in the staff if you pretend (or transpose) that what really is a C is an Eb, or vice-versa.

I've been wanting to know about this for a very long time. It makes absolutely no sense to me that A(440) would be written as a different note for horns.

As I understand, the Tenor Clef can be moved around on the staff lines to better accomodate the range of an alto, tenor, baritone, etc. So I still have no idea about the transposing.