ADVERB (3)

1. as an important constituent;
- Example: "the drapery served organically to cover the Madonna"

2. involving carbon compounds;
- Example: "organically bound iodine"

3. in an organic manner;
- Example: "this food is grown organically"

The Collaborative International Dictionary of English v.0.48:

Organically \Or*gan"ic*al*ly\, adv.
   In an organic manner; by means of organs or with reference to
   organic functions; hence, fundamentally. --Gladstone.
   [1913 Webster]

WordNet (r) 3.0 (2006):

organically
    adv 1: as an important constituent; "the drapery served
           organically to cover the Madonna"
    2: involving carbon compounds; "organically bound iodine" [ant:
       inorganically]
    3: in an organic manner; "this food is grown organically"