Rick: “Who are you really and what were you before? What did you do and what did you think?"
Ilsa: “We said no questions."
Rick: “Here's looking at you, kid."
Rick and Ilsa exchange these words in Rick's flashback to their time together in Paris. Rick remembers this exchange the night he first sees Ilsa in Casablanca, as he drinks alone late at night in the empty bar while Sam plays "As Time Goes By." Rick remembers the days in Paris as idyllic and untroubled. The war had not yet come to the city, and Rick believed he had found true happiness with Ilsa. In the flashback, Rick is lighthearted and smiling, a person altogether different from the heavy brooder we see in Casablanca. In this dialogue, Rick wants to know all about Ilsa, but she rebuffs his questions by reminding him that they agreed not to discuss each other's pasts. This agreement protects the innocence of their relationship, but it also prevents Rick from learning the truth about Ilsa, which might have saved him years of heartbreak. Although the war has not yet come to Paris, it has already spread to Czechoslovakia, where Ilsa's husband, Laszlo, was arrested, sent to a concentration camp, and, she believes, killed. The past is too painful for her to think about, and she most likely also fears Rick's reaction to the news of her marriage.
In Casablanca, whenever Ilsa tries to explain to Rick what happened in Paris, she points out that they knew very little about each other. In effect, this reminder becomes her excuse for the emotional pain she caused him, but it is also a rebuke to Rick. She intentionally maintained his ignorance about her. At the same time, had Ilsa answered honestly, the whole tone of the memory would be different. Ilsa and Rick's simple love would be turned on its head. Rick seems to have a choice: a painful present and a perfect memory, or a complicated understanding of both. As he remembers the Paris days, Rick seems to prefer to keep the memory pure. But eventually he embraces the truth about his time with Ilsa both in Paris and in Casablanca, which is necessary if he is going to move on with his life. He recasts the memory by repeating the line "Here's looking at you, kid" at the end of the film.