A bucket with many holes will quickly leak. In the same way, an idea or suggestion with many flaws or problems will not be successful. A bad plan is like a bucket full of holes. It cannot "hold water" for very long. Hope this helps

I don't know where it came from, but I can tell you what it means. It is usually applied to a logical argument, or a proof, or an explanation. Defects or flaws in the argument can be called "holes." In order to hold water, a bucket needs to be perfectly tight; water will leak through even the smallest holes. So, "your argument won't hold water" means "your argument isn't perfect, there are flaws or holes in it." You can also talk about "a water-tight argument." It is often used in connection with a complicated story, which appears to be a lie; it has holes or inconsistencies; it won't hold water. Some examples of use from a web search include: "That story won't hold water, will it? If it had happened that way, the accused would have told 911 what went on and then stayed at the scene until help arrived." ""This is a very strange tale, Poole; this is rather a wild tale, my man. Suppose it were as you suppose, supposing Dr. Jekyll to have been—well, murdered, what could induce the murderer to stay? That won't hold water; it doesn't commend itself to reason."

I imagine that it comes from the literal idea that if you had a bucket with holes in, then it ‘wouldn’t hold water’. So if your story has holes in (lies), it could be compared to the bucket.