What does “I don’t think we figured in his day at all” mean?

To figure in something something is to be play a part; to be involved. As @Mark points out, in your question, this might refer to intent, or the day's events as the day draws to a close: "I guess he didn't include us in his plans after all"; "I guess we're not going to be a part of his day."

In the US, figure into something is also used. It means "to be included as a part of something", like an activity or calculation. As a speaker of American English, I'd be more likely to use this phrase. They didn't figure into my day's plans at all would mean I did not intend to include them in my activities.

The context in which this sentence was said: Aron meets two girls and one of them invites him to a party that night. He promises to go and then leaves. The girl who invited him is not particularly convinced that he will actually show up and – since she had liked him – she says, somewhat disappointedly to the other girl: "I don’t think we figured in his day at all".

She thinks that he forgot about the party (and the girls) the very second he left, because he had other, more important things in mind.

Though I have not seen the movie, I assume the phrase means either "we had no impact/we weren't a factor on how he planned his day," or "in hindsight, it appears we had no memorable impact of on his day."