What does “Curb your dog” mean?

1. The edge of the sidewalk is a kerb.
Not sure how or when curb came to be used in this context.
Maybe another Americanism.
2. Curb as a verb means to control or restrain.
3. Curb as a noun is a restraint.

As for the doggy poo: not sure how that came about. Have never heard the word curb used in that context.

I think that the "curb your dog" means "restrain your dog" which may include when you spot the errant pooch laying a turd in the street. It has nothing to do with the kerb, which is indeed the raised bit for pedestrians (and in Bangkok the motorbikes and bicycles) next to the road, which is for cars and lorries and buses (and in Bangkok the pedestrians). In the USA this is called the 'sidewalk', in English-speaking countries the pavement. Actually, I think the kerb is the part of the pavement next to the road, not the whole thing.
In England, where dogs are treated in the same way cats were in ancient Egypt, to tell someone to "curb your dog" results in cries of anger and threats of violence, and not from the dog but from its owner and also bystanders who do not know you from Adam. A more subtle approach is to pick up the offending faecal matter, run after the dog's owner and give it to him, or her, and say "your dog dropped this".
'Curb' is a verb, 'kerb' a noun .

Just to add to what Hairy Scot and Brus have said, I would have said just the same as with curb anything else:

curb your temper
curb inflation
curb the spread of the disease

But as 'Curb your dog' is not an expression I was aware of (I don't think it's used in the UK), I had a quick look at Google Images, and it is clear that it is used specifically to mean control your dog's toilet habits, not simply control it's behaviour:

http://www.google.com/search?q=%22curb+your+dog%22&hl=en&tbm=isch&tbo=u&source=univ&sa=X&ei=DI4fU5XpNYqX5AT_xYCYDw&ved=0CDMQsAQ&biw=1018&bih=595

Just to forestall any misunderstandings - kerb (BrE) = curb (AmE), so both Hairy Scot and Dyske are right on that one.

No, no, no. If 'curb your dog' meant 'steer it towards the kerb to do its (ahem) business' you would cry out "kerb your dog". If you mean 'stop it yapping' or 'stop it sniffing the genitalia of folk standing there quietly' you might call out "curb your dog", but in England it would make no difference as it sounds much the same and in England dogs rank higher than humans anyway, and the owners would be mystified.

@porsche - 'the modern world' - does that mean the modern world is restricted to North America? As far as I know, this expression is used nowhere else (for a starter we say 'kerb' in the UK, and so presumably in Australia, NZ etc). The rest of the modern world may have similar laws, but not that particular expression.

So they really do have kerbs in Oz? Just in the settlements?

@jayles
We also have them in Kiwiland, though I did see a sign outside a car accessory store that read "Curbed your mags?", so it looks like confusion reigns in places other than North America. :-))

"kerbing and channelling" with a 'k' seems to be the norm, although I couldn't see whether this is used in the USA

WRT kerbing
The OED has this:-
a. The act of furnishing with a kerb.
b. The stones collectively forming a kerb.

1869 Daily News 2 Feb., The granite kerbing on the sea wall.
1884 E. O'Donovan Story of Merv xi. 124 A canal, with kerbing of brick flush with the roadway.
1885 Law Times Rep. 52 618/2 The requirements of the respondents as to the kerbing.

I didn't know that "curb your dog" was legally defined. That's interesting, and good to know. Thank you.

But what I'm curious about is how that expression came to be; the etymological origin. If "curb" means to take something to the curb to pee/poo, is it ever used for anything other than dogs? If it only applies to dogs, it would mean that this particular usage of the word "curb" was invented only for this particular situation, nothing else. If so, who invented this usage? And, why did s/he invent it? If no such usage of "curb" existed outside of this particular instance with dogs, how could this person expect the public to understand that it means to take the dog to the curb to pee and poo?

And, if it applies only to dogs, why bother saying "your dog"? "Curb" alone should suffice. Just define it as a legal term to take your dog to the curb to poo and pee.

No! It means 'keep (the errant creature) under control', as 'curb' means 'control' (from French 'courber', which is a verb). Stop it from doing what is left discretely unspoken, as being unspeakable anyway.
The kerb is there to separate road traffic from that on the pavement, except in Bangkok where anything goes, really. Dogs just lie there, supine and quite pointless. And no one would tell anyone to do anything with his dog, as that too would be pointless, and most impolite. I have mentioned earlier that in England no one would do so either, as it would provoke outrage.

According to one source (link below) it all started in New York in the thirties, and that ‘Please Curb your Dog’ meant ‘Don’t let your dog do its business on the sidewalk. Let your dog do it in the road’."

On the other hand there does seem to be quite a lot of puzzlement over this. At the Urban Dictionary they suggest two meanings - generally control, as Brus suggests, or picking up after your dog.

Nor are the signs at Google Images consistent - on one, from the Carnegie Hills Neighbors, it follows porsche's idea - "Curb means off the sidewalk"

But one from Chicago Parks District is rather more general, saying - "an ordnance prohibits dogs to be permitted to run at large or commit any nuisance upon any sidewalk, parkway or public park"

Another one covers both Urban Dictionary definitions, saying - "leash-curb and clean up after your dog"

And another - "please curb and pick up after your dog" - that doesn't sound like making it go in the gutter to me.

The there's - "Please curb your dog away from the building", and the rather strange "Private Property, Do Not Curb Your Dog Here" - which sounds as though curb means "make / let it do its stuff"

I'm not surprised people are confused.

And one from Britain - nothing about curbing, of course (we'd be even more clueless as to what it means) - "Dog owners - Please ensure your dog is on a lead and does not foul the amenity areas" - a bit longer, but perhaps a bit clearer?

http://16thwabashdogpark.blogspot.com/2012/03/what-does-curb-your-dog-mean.html

Overheard tonight in a Dorset pub: "I always used to hold doors open for ladies, but then I was accused of kerb-crawling".
It reminded me of this debate, and perhaps of what the kerb is, as the notion of curb-crawling makes no sense at all. It is clear that kerb is a noun, and that is how kerb-crawling is spelled. Curb-crawling suggests the idea that crawling must be stopped, or at least controlled.
If I am expected here to throw light on the matter of dogs and their disgusting canine lavatory habits, then I am afraid that I must disappoint, as my contribution has nothing to do with the faeces of the species.
Cheers!

@Brus - http://en.wikipedia.org/wiki/Curb_%28road%29

Its not confusing at all, it was meant literally "Curb your dog". A person was required by law to walk their dog in the curb (where street meets sidewalk edge). You were not supposed to walk your dog on the sidewalk. That doesn't bother me as much as pet pet owners that assume you don't mind if they walk their pets on your lawn instead of the grassy area by the curb (sidewalk edge). I don't pay a mortgage to have my property used as a toilet for their pets. "Its not ok to walk your pet on my property" You can't pick up urine which kills my grass and you certainly can't pick up soft stool which inbeds itself into the soil and of course the sidewalk; it just smears.

Back in the 70's it was used as get your dog to do its business in the street. There were a lot less dogs around back than and most neighborhoods had a weekly street sweeper. Now it's more or less meaning be mindful where your pup does their business and clean up the poo.

This makes sense that curb means control and picking up what you can. New Yorkers tend to do this well. Gerard Rotonda