The green lines are roads/paths/trails that have been flagged in google maps as having bicycle access. The lines only appear when using Google as the map provider and when you've selected the Trails option on the map, and can be edited using google map maker. You can see them on google maps if you go to maps.google.com, zoom in on an area (your city/town), mouse over the input box floating over the top-left corner of the map, and click the link titled Bicycling from the slide-out menu.
As an example, here is a map of my home town, and here is my home town with the bicycling option checked.
