There really is more than an aesthetic reason for deadheading your Lily of the Nile (or Agapanthus africanus), Susan. Seed production takes a lot of effort on the part of any plant, and most folks would rather that their flowering plants make more and better blooms than waste precious energy on reproduction. Deadheading is an easy way to encourage further blooming. Cut the flower scape from the plant with clean, sharp scissors or shears when all blooms in the cluster are spent, following the stem all the way down into the foliage to where it grows from the plant. Make a clean cut as close to the plant as possible.