Law of diminishing marginal utility - successive quantities of a good consumed will generate smaller amounts of extra utility.
MU can be measured by the price consumers are prepared to pay for a good. The optimum purchase rule states that to maximise total utility, consumers should purchase more of a good, up to where P=MU. Once P>MU it is not worth purchasing, as the price paid woule be higher than the satisfaction gained from consuming it.
The demond carve is derived from (or comes from ) the low of diminshing utility. The low of diminshing utility and optimum purchase rule explain the law of demand, and hence the downward-sloping demand cyrve.