Here's a vid of how it works
From TechCrunch-
“Nearby” Pokemon are those which happen to be close to nearby Pokestops. Tap one of those and the map zooms out to an overhead view, showing you which Pokestop you should head towards. It’s like they looked at the now-banned Pokevision and said “Well, if you can’t beat’em…” The Pokemon you’re looking for should be near that Pokestop; according to most reports, they’re usually within about a block. Pokestops now have circles around them similar in sizing to the one around the player’s — if a Pokemon is within that circle, it counts as “Nearby” that Pokestop.
Pokemon in the “Sightings” section have grass behind them rather than a Pokestop image — this means they’re in the wild and not immediately near a Pokestop, and you’ll have to hunt for them without any built-in guidance. Tapping a “Sightings” Pokemon doesn’t seem to do anything at the moment, and they don’t necessarily seem to be sorted by distance (hopefully this changes)… so you’ll still be walking a bit aimlessly, albeit with the knowledge that it’s not near a Pokestop.