A leaky mode is like trying to fill a bucket with water, but there's a hole in the side of the bucket. Water can still get in and fill the bucket, but some of it will leak out through the hole.
In science terms, a leaky mode is a type of wave that travels through materials, but the wave is not contained entirely within the material. Some of the energy of the wave "leaks" or escapes from the material and travels through the surrounding medium, like air or water.
Imagine you're playing with a slinky, and you stretch it out and send a wave down the length of the slinky. The wave bounces back and forth between the ends of the slinky, right? But if you hold the slinky vertically and send a wave down it, some of that wave will escape out the sides of the slinky, like a side-to-side wiggle. That's a leaky mode in action!
Scientists use leaky modes to study materials and systems, like fiber optics for sending information or sound waves traveling through the ocean. By understanding how the energy of waves leaks out of materials, researchers can improve these systems and make them more efficient.