If you've heard about variable fonts being supported in OpenType 1.8 and want to learn more about the details of how they work, I recommend these two resources:
Start with John Hudson's excellent article announcing the introduction of variable fonts in OpenType 1.8: Introducing OpenType Variable Fonts
. This gives a broad overview that touches on several technical aspects but without getting too technical.
If, after reading John's article, you're ready for more details, the OpenType spec itself includes a chapter that gives an overview, particularly of the variation mechanisms: OpenType Font Variations Overview
. This goes into more detail about how variation of the font's data works. It includes specific details about algorithms used (very nerdy), but also has some not-so-technical descriptions (a little nerdy), with examples and lots of images, to try to explain the key concepts. If you don't care about the really nerdy bits, scan past those. Toward the end, there's an "Interpolation example" section that walks through details about the variation data for a particular glyph (simple -- only 4 contour points to keep the details to a minimum) and how the interpolation of the data would work for a particular instance. If you can follow that example, you should have a good grasp of how the variation mechanisms work.
If you've read these, it will help to get feedback on what parts were helpful or not so helpful, and what key gaps should be covered in these kinds of introductions that were missing. It would be great to get responses in this thread. (For getting answers to specific questions, though, spinning off separate threads would be best.)