I find the concept of subgrid a little hard to wrap my mind around.
I do understand the idea that we want to use nested semantic markup as we like and have elements participate in one grid so we don't have to flatten our markup just for layout reasons. But that is largely handled by display: contents;.
Rachel Andrew explains it in a way that finally clicked for me:
I have an item spanning three column tracks of the grid, it is also a Grid Container with three column tracks - however these do not line up with the tracks of the parent...
If the nested grid columns were to be defined as a subgrid, we would use the subgrid value of grid-template-columns on that child element. The child would then use the three column tracks that it spanned, and its children would lay out on those tracks.
It's not that the parent disappears, it's that it shares grid lines with the parent so that getting internal elements to line up with everything else happens naturally.