A positive externality is a benefit that arises from some economic activity that accrues to the benefit of entities that were not actually involved in that economic activity.
When it comes to roads, many benefits are felt by people who did not pay for the construction of those roads. For example, if a road is constructed in a city far from where I live, I can still benefit from it if I go to visit that city and drive on that road. The building of that road has benefitted me though I did not pay for it. Similarly, if a port city 180 miles from my home builds more roads, prices may fall at stores in my town because transport from that port to my town becomes easier. I benefit from the lower prices that came about because of that road building even though I did not pay for the roads.
In this way, easier transportation that comes with having more roads can benefit even those who did not pay for the roads as a positive externality.
One of the positive externalities associated with constructing new roads is an increase in the efficiency with which vehicles can travel. All vehicles have an ideal speed at which their engines run at the highest efficiency; new roads reduce traffic jams and vehicular congestion that had existed earlier. The construction of new roads reduces air pollution in this way.
Constructing new roads make regions that were inaccessible earlier, easier to reach. This provides an impetus to economic growth in new regions. The reduction in costs for businesses reduces the prices of the final products and benefits customers who may not have contributed directly to the costs involved in constructing the roads.