Viscosity is a physical property of fluids. It shows resistance to flow. In a simple example, water has a low viscosity, as it is "thin". Syrup and tar, on the other hand, have a high viscosity, as they are "thick". A way to test for viscosity is the speed at which the substance runs down a slope. Syrup would reach the bottom very slowly, and water would be much quicker.
Viscosity is used as a way to predict when volcanoes erupt. When the lava comes out very thickly (viscous), there is more chance that it will erupt violently. This is because the lava has a hard time getting out and may burst out when it can. If the lava is thin (low viscosity), then it just flows out like water.
Illustration of a planar Couette flow. Since the shearing flow is opposed by friction between adjacent layers of fluid (which are in relative motion), a force is required to sustain the motion of the upper plate. The relative strength of this force is a measure of the fluid's viscosity.
Video showing three liquids with different viscosities
Experiment showing the behavior of a viscous fluid with blue dye for visibility