Check out this link: http://idioms.thefreedictionary.com/on+the+fly
Student or Learner
Fluent reading is a constant back-and-forth process of inferences, filling in the blanks, testing hypotheses, and constructing meaning on the fly.Try this: "The man went to the window and asked what time the feature began.
What do you mean by "on the fly"? Does it mean "doing something quickly considering other things"?
"while something or someone is operating or moving. I'll try to capture the data on the fly. Please try to buy some aspirin somewhere on the fly today."
I'm not a teacher and I'm not a native speaker of English.
In this specific example it means you have to construct meaning as you go along, while you are reading.
(BrE first language speaker.)