The general gist of it is that you store HTML snippets (e.g. a todo, a list containing, or a project containing lists) in some quick storage medium (in this case Memcached). Each snippet is stored under and accessed by a key that uniquely identifies the version saved (object type + ID + update timestamp). When a new version is cached, the old version stays in the cache, unused, until it is eventially dropped out by Memcached.
Now all you need to do is to ensure that whenever an object or its children change, you update their timestamp (the "touch" part), and if you make a changes to the code, you increment the version key for said cache piece. This way new requests will not hit old cached content.