Acrylic mediums are substances (fluid, gel, or paste) that you can mix with acrylic paints to manipulate the properties of the paint.  The base of mediums is the same as acrylic paint, which is an acrylic polymer emulsion. The difference is that, unlike paints, mediums don’t contain any color pigments. They have acrylic binders in them (just like acrylic color does) and therefore mix and bond well with the acrylic paint (and the pigments within) that you’re using.  The binders ensure that the paint & medium mixture will permanently adhere to the painting surface (and not fall off or crack over time).  There is a large variety of medium types, each serving somewhat different purposes.

With acrylic paint alone, you are limited in terms of how it behaves (how it moves, spreads, blends, dries, and what effects you can create).  With mediums however, you can change various characteristics of your acrylic paints.