It's easy.

"Rust is better for safety than C because it makes it harder or impossible to make certain kinds of mistakes that are easy to make than C."

"What kind of mistakes?"

"There are times when you need to acquire some shared resource. Let's say memory. In Rust, it's easy to ensure you return that memory when you're done with it. In C, it's easy to forget to return that memory when you're done with it. This is called a memory leak, and you might find that eventually there's not enough memory for other programs to run."

"What's memory?"

"Think of a program as a recipe you're performing. Memory then is like working space. Like your counter space in your kitchen. If you run out of counter space, you don't have room to chop up more vegetables or temporarily store your cooked meat or what-have-you. Maybe you ran out of counter space because you left last night's dirty dishes on it. Rust automatically puts the dirty dishes in the dishwasher. In C, you have to remember to do that yourself, and sometimes you forget to."

And so on.

There's an easy explanation as long as you're not expecting them to perform detailed analysis. And I'm not.

edit: eventually you'll get to your limit of simplicity, things like "what is fire?" and maybe you need to say "I don't know, let's find out together!" We all have limits to our expertise, after all.