Viscosity is a measurement of how resistant a fluid is to attempts to move through it. A fluid with a low viscosity is said to be "thin," while a high viscosity fluid is said to be "thick." It is easier to move through a low viscosity fluid (like water) than a high viscosity fluid (like honey).
Most common fluids, called Newtonian fluids (yes, another thing named after that Newton), have a constant viscosity. There is a greater resistance as you increase the force, but it's a constant proportional increase. In short, a Newtonian fluid keeps acting like a fluid, no matter how much force is put into it.
In contrast, the viscosity of non-Newtonian fluids is not constant, but rather varies greatly depending on the force applied. A classic example of a non-Newtonian is Oobleck, which exhibits solid-like behavior when a large amount of force is used on it. Another type of non-Newtonian fluid are known as magnetorheological fluids, which respond to magnetic fields by becoming nearly solid but reverting to their fluid state when removed from the magnetic field.