A medium is the vehicle that painters use to mix with their tube colors when painting, for various purposes such as thinning or thickening the paint, or to add varnish, which can lengthen the life of the paint, or deepen and enrich the color in a painting. There are many mediums available for the painter to use. I recommend reading The Artist’s Handbook of Materials and Techniques, by Ralph Mayer, for an exhaustive report on the different mediums available and their uses, precautions and limitations. Again, the medium used is a very personal thing for each painter.
Acrylic mediums are water-based which aid to alter the acrylic paint in one way or another, such as retarders and extenders, which keep the paint wet for a longer time than normal; and other additives which serve various purposes.