Curb Your Confuse-iasm

There are quite a few dog lovers in our neighborhood. The Petco store up the road is as big or bigger than the actual grocery store...the dog runs in the parks are as busy as the playgrounds...and every day we have to watch our step, lest we inadvertently carry home a gift from some dog whose owner is less than considerate. And I see these signs everywhere:

Right.

So what does that mean, really? It bothered me that I didn't know what those signs meant, yet I was too proud to ask someone
(which would 1. reveal the true word-loving nerd that I am, and
2. reveal, once again, my city ignorance.).

Does it mean "Kick your dog to the curb, as far away as possible from these plants?"
Or perhaps it means "Keep your dog under control," similar to curbing your enthusiasm?

My best guess was that it was an antiquated way of saying, "Please have your dog do its business in the proper place, where it will do the least amount of destruction."

I did a little research and found this from the Pennsylvania Society for the Prevention of Cruelty to Animals:

Curb Training: "Curb Your Dog" signs are found in many cities and townships. Curb training is in the public interest to keep the sidewalks clean. Owners who do not obey can be fined. A Philadelphia ordinance forbids any person to permit an animal to defecate on the sidewalks or other public places in the city (including playgrounds, schoolyards and public parks). This ordinance requires that you clean up your dog's waste as soon as it is deposited.Watch your dog closely as you lead him along, and just as he is ready to go, pull him gently but firmly toward the curb an into the street. It is not difficult. In fact, most dogs take to the idea readily. The same trick may be used when crossing the paths of parks and other public places. A responsible owner considers others, and never permits his pet to foul or damage people's property or areas where children play. Part of being a responsible pet owner is picking up after it! No fancy pooper-scoopers are necessary. Plastic bags work very well.

Yum.
The cultural lessons I learn here are quite something. And we're never getting a dog while we live in the city. No way.