A stable curve is like a really good balance beam. You know how when you walk on a balance beam, you have to be really careful to not fall off? Well, with a stable curve, you can walk on it and not wobble around too much or fall off.
The stable curve is made up of points that are connected together in a certain way. You can imagine these points like the dots in a dot-to-dot picture. You have to connect them in the right order or else it won't make sense.
Once all the points are connected correctly, you get this really cool curve that doesn't wobble or wiggle around too much. It's like the perfect balance beam because it's not too steep or too flat.
Scientists and mathematicians like to study stable curves because they're really interesting and can help them understand how things work in the world. Plus, it's a great way to challenge your brain and make it stronger!