Newtonian fluids have a constant viscosity at a given temperature.
Hence Non-Newtonian fluids have a variable viscosity at a constant temperature. The viscosity will vary with the rate of shear of the fluid. Shear rate is defined as the difference between velocity of parallel faces of a fluid element divided by the distances between the faces. The Viscosity of a fluid is its resistance to flow. To put things in simpler terms, a single grade motor oil is an example of a Newtonian fluid.