My dog does this from time to time-she will be sitting, and lift her front paw…as if to offer to shake hands.
I have seen other dogs do this-is this instinctive (like a pointer freezing and pointing)?
I always wondered what it meant!
It is a friendly gesture with appeasing overtones that dogs will do to other dogs they trust and respect. This is transferred to people. I conjecture that its ultimate origin lies in puppy behavior.
If you watch puppies with older dogs, the pups instinctively lick, nuzzle, and paw at the adults’ mouths. This is to instigate regurgitation (you asked). Wolf packs feed litters of pups by filling their stomachs at the kill site and traveling back to the den and coughing up the meat for the pups. Domestic dogs will do the same thing with kibble, believe it or not.
The pawing gets generalized for other uses later, I am imagining.
I owned a collie and teaching her to shake hands just took putting my hand out one time. I’ve done this to other collies and they all put their paw out.
On the other hand, I have a lab mix and he hates for people to touch his paws. It takes treats to get him to shake hands. None of my kids dogs will shake hands although two of them would probably with some training.
Therefore in some breeds, it may be an instinctive behavior while others it can be a learned behavior.
One of our springer spaniels will do this. She puts her paw either on one of us (usually me) or on her sister springer. I read somewhere that this is a kind of possession gesture, a combination of “I am yours” and “you are mine.” Which sort of matches what Ulfreida said.
I briefly thought about turning this into a “shake” or “gimme five” trick, but I decided that it was such a sweet gesture that I would let her decide when to bestow it on someone and not make her do it on command.
I have a Lab and it was pretty easy to teach him to shake hands since he would instinctively lift his paw when I offered him a treat. The trick was in getting him to lift his paw high enough to shake instead of giving a half-hearted wave of his paw. Now he doesn’t even bother to sit first. He’ll stand on three feet and lift his front paw for a shake. Most of my other dogs, regardless of breed from poodles to golden retriever mixes, also instinctively offered their paws. I had one dog, a golden-Chow mix that I was in line with for her booster shots, turn around and sit, then she patted the head of the dog in line behind her, as if to say, “Nice dog.”
Tried to find a way to say exactly this but Scarlett67 did it better - this is my Baron to a “T” (Shepherd). He will only do it with my husband, my son and I - and I won’t turn it into a parlor trick. He’s very, very possessive of us. And we are of him. 
I would like to know the meaning of another, similar canine gesture.
When our dogs see something that grabs their attention, for example another dog, they often stand, tense, facing the object of interest, ears and tail raised with one front paw raised off the ground.
Usually it’s when they see something in the distance or middle distance, but sometimes also if they meet a stranger dog up close.
I’ve seen lots of dogs do this, but I have never seen it included in any chart of dog body language.
The only time I’ve seen my dog (and keep in mind my dog is somewhat weird) do this is when he’s about to take off after whatever he sees. For example, we have a rabbit in the back that taunts him (long story - him and the rabbit have a history) - when he spies the rabbit sitting just beyond his reach, he does exactly what you described, then the minute the rabbit moves, he takes off to try and catch it (which generally results in my husband almost getting pulled off the deck - this dog is very large. )
It’s kind of like he’s getting ready to “pounce” or something similar.
This is called 'pointing" it is done by hunting dogs, to indicate the location of game 9to the human hunter0.
I forgot to add that our dog always, ALWAYS does this paired with intense eye contact. She definitely wants our full attention. This is an important statement for her.
Yes, and you will see the exact same thing in Border Collies when they are staring at a sheep. I think it is a similar emotion. It has been explained to me that this is a part of the “predation chain”, stalking. My corgi used to do this just before she sprang on a mouse in the grass (which she would invariably swallow whole before I could say “drop that!”