The Law of Diminishing Marginal Utility states that as a consumer consumes more units of a good, the marginal utility, or the additional satisfaction received from each successive unit, declines. This principle is illustrated through the relationship between total utility and marginal utility, where total utility can increase, but at a diminishing rate. The law helps explain consumer choices and demand curves, showcasing that consumers will only be willing to pay less for each additional unit of a good as its marginal utility decreases.