Yttrium aluminium garnet or YAG is a really fancy word for a special crystal material that's made up of three different elements - Yttrium, Aluminium, and Oxygen. Yttrium is a rare metal that can be found in rocks, and Aluminium is a very common metal used in things like foil and cans. Oxygen is a gas we breathe in to stay alive.
Now, this crystal is really special because when you shine a light at it, it glows! This is called fluorescence, and it happens because of the way the crystal is structured. Inside the crystal, there are tiny little spaces called "lattice sites" where certain things, like atoms or ions, can fit perfectly. In YAG, there are a bunch of these lattice sites that can hold another element called "dopants," which are added to the crystal to make it glow when it's hit with light.
The most common dopant added to YAG is neodymium, which is another rare metal. When neodymium is added to YAG and the crystal is hit with light, it absorbs the light and then quickly re-emits it as fluorescence - which is what makes it glow. This is really useful for things like lasers, which can use YAG crystals to emit very high powered light beams that are even used in medicine and some types of surgery! Neat, huh?