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Suppose John is about to consume 4 bananas and 1 orange this week. He is willing to give up some bananas to get an additional increment of some oranges. A decision scientist asks John how many bananas will he give up to get just one orange. John knows that he will be better off by trading one or two bananas for the extra orange; he will be just as well as he is now by trading three bananas for the extra orange; and he will be worse off by trading four or more bananas for the extra orange.
The decision scientist listens to him and concludes that letting go three bananas is what would make John indifferent between the new and the old situations. He is indifferent between consuming (bananas,oranges) = (4,1) and consuming (bananas, oranges) = (1,2).
For the case of two commodities, the utility function U=x^1/2*y^1/2 looks like this: