All dog owners know that when you have a dog in tow, you can talk to just about anyone. I've been at the park with my dog numerous times and have started conversations with people I would probably not talk to under other circumstances. But when you have something in common, you both have a dog, it doesn't seem weird or awkward to talk to a total stranger. Their dog is playing with your dog, or you see their dog doing something cute or funny and it makes you want to tell them!
It is so easy to start up a conversation with someone who has their dog with them. There are so many conversation icebreakers you can use, because of your fur baby; how old is she/he, what breed is she/he, what's their name, where do you walk etc. The list is endless!