The concept of utility is central to the economic analysis of the behaviour of individuals. It is usually defined as the satisfaction that individuals gain from buying products (whether goods or services).
The assumption is that individuals will make choices that maximise their utility. It is not unreasonable to define utility as what individuals are attempting to maximise through the economic choices they make.
The utility of money is important in financial economics. It is usually assumed that the utility of an individual's wealth increases at a declining rate - that an extra pound means more to a poor person than to a rich one. In mathematical terms, the first derivative of the function relating utility to an amount of money is always positive and its second derivative is always negative. This assumption is used to derive the CAPM.
Other assumptions may be made. These include using money as a measure of utility so, by definition, the utility of wealth increases at a fixed rate as wealth increases.
Utility is an important and useful concept, but it is difficult to define in an objective way. Some economic models avoid defining utility as a measurable of numerical quantity, and instead rely on consumer choices between possible baskets of purchases. Other models assume that utility could be measured, but do not suggest any way in which it could be measured.
There are also questions over how well utility maximisation explains altruistic behaviour. Many economists argue that this is utility maximising because of the satisfaction a person feels as a result of altruistic behaviour. This is not universally regarded as a satisfactory answer. A full exploration of this issue would take into studying philosophy rather than economics.