what does "moment-by-moment" mean?
Comprehension is the moment-by-moment construction of meaning that takes place in your mind as you read and process information.

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In this context, "moment" means an incredibly short period of time or an instant.  Some would say it means "a second of time" but it is really shorter than that.

So, moment-by-moment means instant to instant.  You could substitute "instantaneous" for "moment-to-moment".