Lyric discussion by imitationbagel 

This song is a translation of the poem "Breakfast" by Jacques Prévert.

With that being said, I think the song discusses a father and child relationship. As in, the father and child see each other in public every now and then, but the father hasn't and doesn't want any sort of relationship with his child, and will even go so far as to not even look at them in public.

I guess it could also mean a lover who wants nothing but sex and leaves without saying anything, or a child leaving their home for some reason (like war or just in anger). But the father and son (or daughter) aspect is how I interpreted it.

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