Question

Why does a microscope slide need to be transparent?

Answer 1

To let light pass through it and possibly through your specimen.

Explanation:

The Microscope is an optical instrument that uses a phenomenon called Refraction to magnify the image of an object.
In this process light from an object, passing through a lens, is bent and after being collected by your eye is used inside your brain to build a bigger image.

[ Effect of Magnification ]

This allows you to "see" small objects (say the leg of an ant) that normally you wouldn't be able to see; this is because when you look at an ant without microscope the rays of light from her leg are "lost" in the middle of all the other rays coming from every direction and. In a microscope the leg is basically alone without any interference from other objects and the light coming from it is very bright.
So the idea is to have:
a source of light that sends its rays through your specimen and then passing through the lenses (forming your microscope) to your eye.

But the leg of the ant has to be placed somewhere (to avoid it flying away or falling inside the microscope) and you need a transparent support to allow the light from the source to pass.
On top of it if you try to look at a specimen that isn't trasparent you will not be able to make light pass through it and magnify it (the leg of the ant is very thin so it will be probably almost transparent).