Imagine you have two friends - Friend 1 and Friend 2. Friend 1 tells you that they are going to open a lemonade stand, and Friend 2 tells you they are going to open an ice cream truck. You want to know which friend is actually going to open their business, but you don't want to ask them directly.
So, you come up with a plan. You give both friends a rock and a piece of string. You ask Friend 1 to tie their rock to the end of the string and swing it back and forth. You ask Friend 2 to tie their rock to the string and hold it very still.
Then, you stand in an open field and ask both friends to swing their rocks towards you. The light from the sun hits both rocks and reflects back towards you. When the light waves from Friend 1's rock and Friend 2's rock combine, they will either add together or cancel each other out.
If the light waves add together, you'll see bright spots of light where the waves aligned. If they cancel each other out, you'll see dark spots. By looking at where the bright and dark spots show up, you can tell which friend is swinging their rock back and forth and which friend is holding their rock still.
That's kind of how a Mach-Zehnder Interferometer works. Instead of two friends with rocks and string, you have a laser and mirrors that send the laser light down two paths. When the light waves from both paths come back together, they either add up or cancel out. By looking at where the bright and dark spots show up, scientists can learn things about the properties of the light or the materials that the light has passed through.