For instance, if I wrote "word" with poor handwriting, and you couldn't tell what it was, but then I told you that it said "word", and you replied, "Ah, I see how it could say word." Is there a word describing this type of after-the-fact realization?
I like the informal definition of “click” (from OED):
Become suddenly clear or understandable.
‘I wasn't used to such good treatment, then it clicked: we were wearing suits’
If someone 'sees' something after an explanation it is 'enlightenment'.
The action of bringing someone to a state of greater knowledge, understanding, or insight; the state of being enlightened in this way. Also: an instance of this.
1990 Shareware Mag. Nov.–Dec. 9/1 This column is a place to network with other users for mutual enlightenment
Elucidate (verb) or elucidation (noun). Both require explanation to bring about a sense of greater learning.
Merriam-Webster on elucidate:
(transitive) : to make lucid especially by explanation or analysis
(intransitive) : to give a clarifying explanation
Here's two examples based on what you wrote:
At first I didn't understand the inscription, but you elucidated it for me.
You provided elucidation to me, and for that I thank you.