What does characterization mean in a genomics context?
There's no technical definition for "genetic characterization". It is simply a phrase used by authors based on the normal meaning of the words: (1) having to do with genes and heredity, and (2) describing the essential character.  Of course the bounds of the genetics and the essence of their nature are entirely in the eye of the author and reader, so no particular definition applies across all papers in genomics (or in other fields).