The ratatouille is a traditional French dish. It is safe to assume that the critic had had it when he was a kid (like a paella if you are Spanish, apple pie for an American kid, tagliatelle alla bolognese for an Italian... and my list of cliché dishes goes on and on).
The Epic Win for Remy is to offer the critic a dish that is popular in their cuisine (thus, odds are that the critic guy had had that before), do it offering something new (those instructions about cutting ingredients and preparing the plate in a different way) and fancy (fancy enough to be successful and interesting for the menu of the restaurant) and yet, get a flavor that triggers an emotional reaction in the critic, thus making him enjoy food, something he had long forgotten.

Remy's version of the dish is actually called confit byaldi.