Load-link/store-conditional is a way for a computer to make sure nobody is messing around with some information while it's trying to update or change it. Imagine you have a toy and you want to show it to your friend, but you're worried that someone might come and take the toy away from you before your friend has a chance to look at it.
So instead of just giving the toy to your friend, you say "Hey, hold on a second, let me make sure nobody takes my toy. I'm going to look at it really quickly and remember exactly how it looks. Then I'm going to give it to you and ask you to look at it too. But before you do, I'm going to check again that nobody took or changed the toy. If everything looks good, you can have it and we'll both be happy!"
That's basically how load-link/store-conditional works in a computer. When the computer wants to change or update some data, it first "loads" the data into a special place in its memory where it can remember exactly how it looks. Then it goes ahead and does whatever it wants with the data, like changing some numbers or adding some text.
But before it "stores" the updated data back into its original location, it checks one more time that nobody else changed or "took" the data while the computer was working on it. If everything looks good, then the computer goes ahead and "stores" the new information back into its original location. If not, the computer will know that something went wrong and it will try to fix it before it tries to "store" the updated data again.
So just like you with your toy, the computer uses load-link/store-conditional to make sure nobody messes with its information while it's trying to work with it. And just like you and your friend, the computer and its programs can be happy knowing that they're working with the correct and up-to-date information!