The term medium has various meanings. For starters, it's used for the substance that binds the pigment in paint. In acrylic paints, this is a synthetic substance. In oil paints, it's a natural oil such as poppy. In tempera, it's egg yolks.
A medium can also be something used to change the consistency of the paint. For example, a gel medium is used to thicken paint for impasto.
To add to the confusion, the term medium is also used to describe a category of painting or simply a type of paint, such as oil painting, acrylics, or watercolors.