Marginal utility refers to the benefit or satisfaction that a consumer receives from a product. Economists use marginal utility when determining how much of a product a consumer will buy.
A basic example of marginal utility is to compare two people buying the same product. You buy one ice cream sandwich and your friend buys a box of 10 ice cream sandwiches. If you buy one more ice cream sandwich, then your total number of ice cream sandwiches increases by 100%. When your friend buys another ice cream sandwich, her total number of sandwiches changes to 11, which is only a 10% increase. The smaller percent increase, the smaller marginal utility and vice versa. In this scenario, you have larger marginal utility than your friend. The more of the same product you have, the smaller the marginal utility of the product becomes, until you don't need any more of the product.
When compared to the law of diminishing marginal returns, the major difference is the focus on production rather than consumption. While both concepts are concerned with the ideal amount of something, the law of diminishing marginal utility focuses on input and output of production rather than amount of consumption (like in the concept of marginal utility).
An example of the law of diminishing marginal returns can be applied to a small business. You are a small greeting card manufacturer, and you have ten employees who have a variety of responsibilities that help you produce and sell the cards; your company is running optimally with these 10 employees. The law of diminishing marginal returns states that, if all other production factors remain constant (i.e. resources, production tools, etc.) and you hire more employees, the company's efficiency and "returns," i.e. income, will decrease or diminish.
Although the two concepts are related, marginal utility focuses on how much of a product a consumer will use, while the law of diminishing marginal returns focuses on how much of a certain production factor to use when producing that product.