The strings are anchored at each end, and need room to vibrate without touching the frets (which would cause a buzz). The actual waveform is quite complicated, but suffice it to say, the strings need more room above the frets in the middle of the string than they need near the ends (since the ends are fixed).
If the neck has back bow (convex, when looking towards the fretboard), frets in the middle of the neck will appear higher than the saddle and nut... the strings might even rest on the middle frets. The strings will buzz, almost guaranteed....
If the neck is dead straight/flat... strings will (usually) be closer to the frets, requiring less pressure to fret. Since strings will be stretched less when fretting, intonation might be better. On the other hand, a straight/flat neck requires a light attack (fingerpicked, or good pick technique) to avoid having the strings hit the frets, causing them to buzz.
Adding some relief (forward bow, concave when looking at the fretboard) gives the strings more room to vibrate w/o touching the frets. Too much relief will make it harder to fret as you move up the neck, as well as throwing off the intonation.
So, its sort of a trade off... you want sufficient relief (in the form of forward bow) so the stings can vibrate cleanly, without so much that fretting is more difficult and intonation is affected.
Once you have the relief properly adjusted (to factory spec, or your preference), you then set the action at the (nut and) saddle... remembering that lowering (or raising) the strings by 1/64" requires lowering (or raising) the saddle by TWICE that amount.... 1/32" in this example.