What does Singer mean by "marginal Utility"? What would it mean to give to others up until the point of marginal utility?
The term "marginal utility" was created circa 1890 as an economics attempt to understand and fairly decide the price of things. It was proposed by Peter Singer also as a way to discuss morality and affluence in times of famine. In 1971, Singer wrote "Famine, Affluence, and Morality", where he proposed marginal utility in a similar use, but for a different scenario.
In Singer's own words,
it follows that I and everyone else in similar circumstances ought to give as much as possible, that is, at least up to the point at which by giving more one would begin to cause serious suffering for oneself and one's dependents - perhaps even beyond this point to the point of marginal utility, at which by giving more one would cause oneself and one's dependents as much suffering as one would prevent...
This excerpt explains what Singer means by giving to the point of marginal utility (i.e., giving to the point at which more than that will cause giving to backfire and harm you and yours even while helping others). Also, you can see in the excerpt that Singer uses his terminology in a flexible way.
In economics, marginal utility means the point that diminishes the level of satisfaction when a product keeps being tried over and over. A good example of marginal utility is found in eating.
In the world of competitive eating, the "athletes" claim to be hungry when they start the competition. However, they also say that by the time they reach the 5th to 8th food item, the taste becomes tiresome, the body begins to reject the food. The competition really starts when they just swallow the food as best as they can.
So marginal utility refers and applies to business and indicates the level at which one more good is diminished in utility or benefit. Giving to others to the point of marginal utility refers and applies to alleviating suffering by giving and means to give up to the point that one more measure of giving would cause suffering to yourself and your family at the same that it alleviated suffering in others: the objective for giving to marginal utility is to reduce suffering without creating new suffering in your own dependents.