Both of these things have to do with what people want and how much of it they want. The law of diminishing marginal utility tells us that we will be willing to pay a lot for the first unit of something that we buy, but we will be willing to pay less and less for further units. Indifference curves are representations of the combinations of things that we will be satisfied with having.
In order to understand the law of diminishing marginal utility think about what would happen if you came upon a food truck when you are extremely hungry. Let’s say that burritos at this truck cost $2 each. You are so hungry when you get there, that you would be willing to pay $5 for the first burrito and maybe even for the second. You get a lot of utility (value) from those burritos because you are so hungry. But now you’ve eaten two burritos and you’re not that hungry anymore. A third burrito wouldn’t have so much utility for you. The utility you get from eating burritos drops as you eat more of them. This is the law of diminishing marginal utility.
Indifference curves are related to utility. Indifference curves show different possible combinations of goods that would all have the same utility for us. Let’s say you are at a barbecue and you can have as many hamburgers and/or hot dogs as you like. You may not really care which of these you have. So, you might be just as satisfied with 2 hot dogs and one hamburger as you are with 2 hamburgers and one hot dog. Your indifference curve would include those two combinations because they have the same utility for you.