The citizens of America are given certain rights and opportunities to enjoy liberties and freedom and to have a peaceful life. But in return of these rights, the citizens have some responsibilities that they have to fulfill not only towards them but also other people.
They should work not only for their own benefit and welfare, they should also take into the considerations, the welfare of the society and the people who are living in the society.
The best way according to him is to make a good fence. The poem's final lines says that good fences make good neighbors. That can mean that if you stick your nose in your yard you will have good neighbors. Of course, this is all figuratively and refers to much greater things in life.