My subtle hint above may have given away the fact that the word comes from a larger log that was put at the back of the fire to help keep it going while you continued to add smaller pieces from time to time. Not unnaturally, the OED says the word came to imply having something in reserve. It’s interesting how the meaning of words can change over time, in that it now has a flavour of having too much of a build-up of something, a sense of an accumulation of many jobs or things that will be difficult to clear – which of course is a quite different thing.
It reminds of the word ‘want’ which I sometimes come across in my historical research. From Victorian times and earlier it generally meant a lack of something – ‘There is a want of sailors for the navy’, ‘I didn’t buy it because I only had five shillings and wanted the additional one that it cost’. I first became alerted to this distinction many years ago when a slimy politician tried to use it to get out of a hole he’d dug for himself. I can’t remember what the context was, but his use of ‘want’ as ‘I’d like to have something’ had embarrassed him for some reason and he tried to say he merely meant ‘I lack something’. Everyone knew he was lying, and he knew everyone knew he was lying but said it with a kind of smirk. So as well as teaching me about the word ‘want’, it also taught me a good lesson about politics and politicians.