A utility curve is the relationship between utility and the supply of something that increases utility, or the graphical representation of that relationship.
This is a key concept in economics. In financial economics the important utility curve is the one that describes the utility of wealth.
The shape of utility curves is an important question to which economists seem unable to find satisfactory answers. Much financial theory assumes that the marginal utility of money decreases, so the utility curve for wealth increases at a decreasing rate as wealth increases — i.e. it flattens as it climbs.
Economists make other assumptions in other contexts, including measuring utility in terms of money, so there is a certain inconsistency in assumptions.
For a slightly more detailed discussion, see utility.