A transformation is just the concept of changing some number to another. Translation is a form of transformation. If you have a coordinate X as 100, and you want to move positive 25, you create a formula of X + Movement. This is a transformation. It can be anything, but mainly the interest is in the kinds that move things in meaningful ways on a screen or coordinate space.
Another example is scaling, which would be multiplying some number. If these are coordinates that draw some shape, it will create the illusion of the shape growing or shrinking, or zooming if everything around it is being scaled too.
Matrices are just a mathematical device. They're collections of numbers that can represent a series of multiplications and sums in a compact form. Typically in games the things that get packed into them are the transformation values for scaling, rotating, skewing, and translating. The order is important when creating this "transformation" matrix.
That's a very surface level explanation, but there is quite much more to say. They're certainly topics worth studying for game development. In the end it takes some tinkering with them to see what's going on.