To answer your question: it is primarily about figuring out how to position the H1 in visual relation to the content division in which it currently resides, if it ends up not actually being in there. Such things as this are still open to development. It should be in there, to my mind. I don't want two navigation lists in between the H1 and its sub-heading: that just seems odd and messy. And I hate messy.
In the case of the main nav list, it is a way to conveniently/reliably position a list AND a heading together in a particular part of the page. Which is to the left of the content in this case, as I already mentioned. If I don't use a heading above the main nav, then I won't need to use the div and I might remove it.Though, just to rag on you a bit (not entirely serious -- not sure if those are placeholders or if you'll have them in the final code) if the accessibility menu going to be a UL, why have the DIV? If the main menu is going to be a UL, why have the DIV? Both are perfectly good block-level containers so don't waste a div on them for NOTHING -- especially the one you won't display for screen/print.
In the case of the skip links list, the div contains, or will eventually contain, a logo and/or website title. Again, it might be removed later if the design doesn't need it. But at the end of the day, if I want to use a div, I will.