This law states that marginal utility declines as the consumer acquires additional units of a given product.
For example, suppose you absolutely love hamburgers. So you go to a burger joint and order one burger. That burger gives you 30 utils of satisfaction. You finish off that burger while still standing at the counter. The amazed cashier asks if you want another. "Sure!" you say and buy another - but this gives you only 23 utils. You eat this burger in about five bites, when the cashier asks if you want yet another. What the hell, you think, I'm getting a little full but I just love those burgers! This one however only gives you 4 utils.
This particular burger takes awhile to finish with several moments where you stop to let things settle. Now you're full. When you finish this third burger, the cashier yet again asks you if you'd like another. Well, considering you've spent almost all your money, are really full, and have to use the bathroom, the utils you'd receive from that next burger would be a whopping negative 10. So you decline.