The yellow and blue lines around the map are the borders for the map and camera respectively (as matic's already pointed out). Patches of squares on the terrain itself show up when you show display the pathing layer; default hotkey combo to toggle it is Shift+H or you can select View -> Show Layer -> Pathing.
Pressing H or selecting Layer -> Pathing will toggle the pathing brush in the Terrain Editor.
- Terrain that is painted red (No Pathing) is non-pathable and cannot be crossed by ground units (but air units can still fly over them), nor can they have structures built over or have any abilities that require walkable pathing be able to be casted on (i.e. Thor 330mm Barrage Cannons).
- Yellow tiles (No Building) are pathable by ground units but cannot be built on (useful for Tower Defence maps).
- Green tiles (Ground) can be built on and crossed by units. Green tiles will allow you to create pathing instead of blocking it, so you can create fake 'bridges' out of doodads and then paint them with this pathing tile to allow them to walk over an area that would otherwise be unpathable.
- Blue tiles (No Burrowing) prevent units that have the Buried flag from being there, so Widow Mines or Zerglings would be unable to burrow on terrain that has been painted with this.
Dynamic Pathing Fill simply fills the cliff layer that you've clicked on with No Pathing tiles. Note that it won't fill the same entire cliff layer if a part of the pathing map is cut off (if you have a canyon in the middle and use this tool on the left side of it, only the left side will be filled).
No Fly Zone prevents air units from flying in that area, but do not prevent ground units from moving into them. The NFZ's cylinder has Hard Radius and Soft Radius parameters; Hard prevents air units from completely flying into that section, while Soft will slowly push an air unit back if it flies close to it. The Hard radius should always be less than or equal to the soft radius.