Good question, not sure I’ve got an answer. Just a term I’ve heard a lot, always sounded like it was doing something on the molecular level. Which I guess everything is. I think it’s this. When you stretch the milk, you’re trying to (about) double it in volume with tiny bubbles (microfoam). If the bubbles are too big, that’s foaming the milk. I think. Lance will better explain it. But foam like that is the way it’s done in most of Italy (from my limited experience). It’s just a different way of doing it.

Stretching the milk simply means increasing its volume by incorporating air. If you start with, say, 100ml of milk, when you’re finished, you should have perhaps 150ml (depends on the milk, the fat percentage, the drink, etc). But that is all that it means.