Large cardinal property

Okay, so imagine you have a really big number, like 1 million. Now, imagine you have an even bigger number, like 1 trillion. When we talk about large cardinal properties in mathematics, we are talking about numbers that are even bigger than 1 trillion, much much much much much much much much much much much much much much much much much much much much much much much much much much much much much much much much much much much much much much much much much much much much much much much much much much much much much much much much much much much bigger!

Now, why do we care about these really big numbers in math? Well, sometimes we need to prove things are true or false, but we don't have enough information to do so with just the numbers we know about. So we make up new numbers that are even bigger than the ones we know about, and we use them to help us figure out whether something is true or false.

These really big numbers are called "large cardinals" because they are like special cards in a deck of cards that are really powerful and can help you win the game. But just like you can't use the powerful cards all the time, you can't use large cardinals all the time either. They are really useful for some math problems, but not for others.

So in summary, large cardinal properties are properties of really really big numbers that mathematicians use to help them solve certain problems in math. They are like special cards in a deck of cards that can be really helpful, but only in certain situations.