Acrylic ink is, as the name suggests, a form of ink based on the same ingredients as acrylic paint. It uses acrylic binder rather than the water of traditional inks. It's a form of acrylic paint that is as runny or liquid as ink, with the strong color intensity you'd expect from artist's quality acrylic paint.
Acrylic ink is even runnier than fluid acrylics. (Think water compared to melting ice cream.) It has a water-like consistency like traditional calligraphic or drawing inks, but, unlike water-based ink, acrylic ink is insoluble when dry (as acrylic paint is).