"Flying in" a part is just a fancy name for copying and pasting the same section into another section of the song. A typical example might be taking a repetitive set of vocal tracks originally recorded in, say, the first chorus of a song, and re-using that same recording in the second and third choruses as well. Assuming a bar & beat grid, this is easily done either by selecting & Option-dragging the Regions from their original location to the other location(s), or by selecting them and copy/pasting them (the video below shows this being done with a bass track around 2 minutes in, using the marker track as a guide).
Of course, things can get more complicated.. Even if the performances were recorded to a click, if the parts are not quantized there may be differences in timing between the sections that can show up against other parts not flown in. And if the recording is not click-based, the Tempo may be different. Of course, issues like this can be dealt with nowadays by using Flex and Smart Tempo, but that may require a little extra work. Logic even has a few dedicated Edit menu commands to move whole sections (Edit > Cut/Insert Time > Copy Section Between Locators). And that's not to mention musical considerations, like whether it's more appropriate in a particular song/arrangement to re-use the same repetitive part multiple times, or perform it fresh for each repetition.
In the screenshot below (from another Logic video) you can see what looks like a repetitive part that's been flown in from the first chorus(?) to the second and third, a classic application for the technique..