Imagine you are a kid and one day, your parents tell you that they're going to do something for you that is in your best interest. This means that they are going to do something that they think is good for you, even if it's something you might not like or understand right away.
For example, maybe your parents decide it's in your best interest to eat some vegetables even though you might want to eat only candy. They know that vegetables are good for you and will help you grow and stay healthy.
Now, let's say you are in a situation where you can't make decisions for yourself, like if you are too young or sick to do so. In this case, other people might make decisions for you that are in your best interest. These people might be doctors, lawyers, or even judges.
They will look at your situation and try to figure out what would be the best thing to do for you. For example, if you are sick and need medicine, the doctor will prescribe what they think will make you better. If you are in a court case and the judge needs to make a decision about where you should live, they will try to figure out what would be the safest and happiest place for you.
So, when someone talks about "best interests," they mean figuring out what would be best for someone, even if that person can't make the decision themselves. It's like your parents making a decision for you, except it's someone else doing it, and they're making the decision based on what they think is best for you.