For example, when grocery shopping, if I cross an item, it disappears straight away from my list. Lets say I have 50 things on my shopping list, including "Salt" – If I check that item, "Salt" disappears from my view. It's clean, but it becomes a hassle if I later forget whether I've already checked "Salt" or if I just forgot to write it down, or if I did and already checked it but forgot about it.
I don't suffer from dementia yet, but it's handy to know what you've accomplished on a particular day; to see aaaall the things already crossed over. It motivates you to keep going!