Okay so, imagine you have two magnets. If you put the north pole of one magnet near the south pole of the other magnet, they are going to be attracted to each other and stick together. But if you put the north pole of one magnet near the north pole of the other magnet, they are going to push away from each other and not want to stick together.
Now imagine you have a special type of material called a superconductor. When the superconductor is very very cold, like -271 degrees Celsius, it can do some cool things. It can conduct electricity without any resistance, which means the electricity can flow through it without losing any energy. This is kind of like a car driving on a road without any bumps or potholes slowing it down.
So let's go back to the magnets. If you have a superconductor near a magnet, something interesting happens. The superconductor doesn't want to let the magnetic field from the magnet go through it. It's kind of like a wall blocking the magnet's field from getting through.
This is where Josephson penetration depth comes in. It's a way to measure how thick that "wall" of the superconductor is. The thickness of the wall depends on things like how cold the superconductor is and the type of material it's made of.
Scientists use this measurement to understand how superconductors work and how to make them better. It's like measuring how thick a blanket is to know how warm it will keep you.