Diminishing marginal utility implies that marginal utility from one additional unit is inversely related to the number of units already owned. For example, the marginal utility of one slice of bread offered to a family that has five slices will be great, since the family will be less hungry and the difference between five and six is proportionally significant. An extra slice offered to a family that has 30 slices will have less marginal utility, since the difference between 30 and 31 is proportionally smaller and the family's appetite may be satisfied by what it already has. As a result, rather than having a lot of one good or a lot of another one, one prefers having some of both. In the case of perfect substitutes this does not apply, in the case of perfect complements it applies most.
Diminishing marginal utility is a very common assumption in economics, but it is not universally assumed. It corresponds to convexity of the indifference curves.