How much of your conversation is understood by your pet? Suppose you talk to them all the time. Does that increase their vocabulary?
Yes.
That is how all dogs are trained to respond to verbal commands.
I’ve heard that an eight-year old dog has a comprehension vocabular comparable in size to that of an eight-year old human, but I don’t recall where I heard that, so don’t take my word on it. Regardless, I can say with certainty that my old dog Bear (rest his soul) understood about fifty different words for “walk”.
Our dogs (dachshunds, not exactly the dot in dot com) understand a few words well – walk, car, dinner, treat, etc. – but they use a lot of non-verbal clues – if I’m at the top of the stairs they know it is either the car or a walk, and so on.
My in-laws’ dog, a Portugese water spaniel, clearly understands the word “walk” even when spoken in passing, so she definitely knows the word without other clues.
Working dogs, sheepdogs are the classic example, seem to be the champions – they understand quite a list of commands. But I’d be surprised if their vocabulary is more than fifty words or so. I’m certain it falls well short of an eight-year old human’s vocabulary which is well into the hundreds, if not thousands, of words.
Apart from vocabulary, I doubt they “understand” much of what is said to them. But they certainly respond to the tone in which it is spoken, which is usually all that anyone really wants from a “conversation”. If I could pick up the emotion behind the words as well as my dogs do, my wife would be much happier with her husband. (But I always get the last words: “Yes, dear.”)
Now cats – they probably understand every single word you say to them. They just don’t care.
Truer words were never, er,…posted. 
Either one of our 2 cats can be sitting near you, looking in the opposite direction. But say a certain “key” word…Chicken, or tuna…and their head snaps toward you at lightening speed. They know what you said…and now they care!
I don’t have any empirical evidence to back this up, but my experience with my cat is that he understands some things I say, but mainly because of the situational cues, tone of voice, time of day, that sort of thing, if I say something with an inappropriate tone of voice, he goes with the tone and not the content.
The only things he doesn’t ever understand are ‘Yes, you WILL eat the dry food’ and ‘No, don’t pee on the bed’.
Two great “Far Side” cartoons:
In one panel, a dog’s master is scolding his dog: “Bad girl, Ginger. You shouldn’t pee on the carpet, Ginger. Ginger, I can’t believe you did this.” In the next panel is what the dog hears: “blah blah, Ginger. blah blah blah blah blah blah, Ginger. Ginger, blah blah blah blah blah blah.”
Larson did a follow up with cats. In the panel of what the cat hears is an empty speech balloon. :D:D