The clip is from an earlier flashback scene when young Vito and his family are heading home from their trip to Italy. Vito is holding Michael at the window and helping him to wave goodbye.
If I recall it's shown either over or just before we see that closing shot of Michael sitting by himself.
The purpose is probably similar to that of showing the birthday party scene with all his brothers. It's a nostalgic but tragic moment, meant to further instill in the audience the sense of isolation and loss between Michael Corleone then and now.
I think.
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