I've always called it plug welding too, but I guess the correct term is rosette welding. As the guys said, it is welding through a small hole to fill it up with weld and in the process weld a piece of steel under it to the top piece.
It is not meant in most cases to be a final strong weld, but rather just sort of a tack weld to hold something in place until you fully weld it.
Here is how we put backers inside a rail so we can burn a good hot weld into a joint. First we drill a couple of holes in only the top piece.
Then we clamp the second piece under it.
And finally, we weld down into the holes to join the two pieces together.
Plug welding does not have to be in holes that small. I use it alot, to hide welds in furniture. We weld them up and grind off the top of the weld, and no one knows the weld is there. But Don's pictures are dead on.