A. He backs.
B. He is back.
C. he will be back
What is the difference in meaning between these?
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Back in B. and C. is a locative expression meaning, approximately, "once again at the place he left earlier". The Cambridge Grammar of the English Language would classify it as an "intransitive preposition", meaning one which does not take an explicit object. Its real-life object can be inferred from context; we have no way of knowing whether back here or back there or back home is meant.
Locative expressions may serve syntactically as nominals, adjectivals or adverbials; in these two sentences, where it is the complement of the complement be, it is best understood as an adjectival, naming the location of the subject. The two sentences differ only in tense—the time to which they refer.
Backs in A. is an intransitive verb meaning "moves backward". It is very unusual to see it by itself this way; ordinarily it would be followed by a locative expression describing a goal or path: He backs up, He backs away, He backs into the corner, or something of that sort.