What does it mean when a dog.. ?

That means the dog loves and accepts you. Perhaps the owners don't give this dog much attention, and you happen to have struck just the right chord with him. I'll bet the dog would go straight home with you, if given the chance!

I think, usually, the dog wants to get up to the level where it can be "face-to-face" and this is the easiest way. If you were to stoop down, then the dog would be at face-level and I'm guessing, would lick your face.

It is just a matter of lack of proper training. Dogs should be taught not to jump up on people. It's just an untrained dog.

The dog wants attention. It's not rocket science.

Sounds like he just wants some of that good rubbin'. Carry on.

Usually a poorly trained dog.

Basically it means it's not been trained not to do that.  Jumping up is a no-no for me.  I'm small and wouldn't want a big dog, who is not mine especially, jumping up like that.

Dominance....Attention seeking.....Greeting.......it all depends on the individual dog as to what this action by the dog means. 

If the dog is `intending` to keep its paws on you, as you state, the dog is probably a dominant natured dog demanding some attention from you. That`s not to say there is any aggression involved, just Bossiness.

It means they're untrained dogs and potentially aggressive as well. Are these YOUR dogs? If not why are you going into someone's fenced yard?

i think that’s just their way of showing they like you, although my dogs like to hug!

It doesn't 'mean' anything...just that it is trying to get level with you so say hello.   I personally don't allow that but some people do.