There is a good definition of diminishing marginal utility, and some great real world examples, on the Beyond Cost Plus website, but it's straightforward once you get past the "utility" part.
What is meant by utility really depends on the product being discussed. The utility of ice cream is pleasure - it tastes good. And that pleasure tends to diminish with each spoonful – each one provides just a little less pleasure than the one before. That is diminishing marginal utility.
Of course it does not apply to everything. Fuel for example – the utility of fuel is the ability to move your car a certain distance. Each gallon of fuel provides the exact same amount of utility, meaning it gets you just as far, as the one that came before it. That is one of the reasons why gas stations don't really offer volume discounts on fuel.
They like the concept though, and they definitely use it inside the station where the largest soda from there fountain might cost just a little bit more than the one half its size. They recognize that the extra soda offers less pleasure than the first few sips, so they are offering it to you at a reduced price. And of course there are higher margins on the soda that allow them to do that.
The Beyond Cost Plus website includes many other definitions and examples of pricing concepts.