Consider the below sentence (source)
The next day, Wednesday, saw Robert become more frustrated.
I can understand the structure of the sentence. I guess it is a kind of deletion. Am I right?
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While AlanCarmack's answer is formally correct (it is saying that the day saw the change in Robert's mood), I think it is more helpful to think of it as an impersonal construction.
I don't think it's helpful to treat it (as V.V. would have it) as personification of the day. It's simply an idiom for events that are observable, but for which no specific observer is necessary.
The standard impersonal form in English is to use the third-person pronoun "one":
The next day, Wednesday, one saw Robert become increasingly frustrated.
However, despite being grammatically impersonal, this still implies the existence of a person making the observation. We can better preserve the full meaning of the original if we refer to the "seeing" as possible rather than actual:
The next day, Wednesday, one might have seen Robert become increasingly frustrated.
To my mind, at least, this has precisely the same meaning as the original sentence. Its style is rather more overwrought and flowery, though. The original sentence is, to me, a perfectly ordinary phrase. (It is formal perhaps, rather than conversational, but it's not literary either.) Therefore I suggest seeing "the day saw..." as an English impersonal idiom.
The next day,Wednesday,(Subject) saw (verb) Robert become (object +infinitive construction ) more frustrated (complement ).
It's the same structure as I saw him cross the street.
The author used a stylistic literary device,a kind of a metaphor called personification.
Obviously the day cannot literally see Robert become increasingly frustrated. Neither may a person see Robert's internal emotional state change. In this case, "saw" acts more like "oversaw". As in, it happened during Wednesday's watch. That is, while Wednesday's sun was shining on Robert. The fact that the observation is attributed to a non human construct may imply that it went unnoticed, or at least was not understood for what it was, by any person. Similar to the phrase "God knows what is in his heart.", it is less about what God knows, and more that no human can know what is in his heart.