Is there a single word that means 'adding more details' or 'enriching with information'

It depends so much on the context, but I'd go with "elaborate."

As in:

… the National Weather Service … advised all citizens in New Orleans's water-filled neighborhoods “to take the necessary tools for survival.” The Weather Service elaborated: “Those going into attics should try to take an axe or hatchet with them so they can cut their way onto the roof to avoid drowning should rising flood waters continue to rise into the attic.” —Christopher Cooper & Robert Block, Diaster, 2006

In light of your updated question, I think you should also consider "illustrate" and "specify."

Enrich, enhance, embellish, ameliorate, or perfect would do.

The best I think of is "refine". From Wordnik:

v. To use precise distinctions and subtlety in thought or speech.

v. To improve in accuracy, delicacy, or excellence.

v. To affect nicety or subtlety in thought or language.

EDIT (AFTER THE QUESTION UPDATING)

"Specify" (from Wordnik):

v. To state explicitly or in detail: specified the amount needed.

v. To include in a specification.

v. To state as a condition: specified that they be included in the will.

It depends on the precise context, but you might want to consider expand (on).