Most content you share probably comes from RSS feeds, e.g., from your own (or others') blogs, YouTube channels, etc. This is great when you want to easily share content published elsewhere, but sometimes, you just want to queue up organically content of your own; i.e., content that you write yourself. That's what Queued Posts is for. So when we say "organically crafted tweets of your own," we mean posts that you yourself are manually writing, as opposed to content from RSS feeds.
This is an important feature to consider, since Queued Posts helps to ensure your posts are always dynamic and alive, mixing together both RSS-fed content as well as your own organic content.