Viscocity is the measure of internal resistance to shear or tensile stress. We conceptualize this internal friction as thickness of a fluid. Thus molasses or honey have high viscosity while water has a much lower viscosity, and alcohols have even lower viscosities. Thus, shaking the diluted shampoo might give an indication of the amount of soap, but does not tell you about viscosity. In order to measure viscosity, scientists use a viscometer. Basically it is a long, thin, glass tube and we measure the time it takes to run down the tube. The longer it takes, the more internal friction, and thus the higher the viscosity.

Viscosity is the difficulty with which a fluid flows - basically, the more viscous something is, the more it is like a solid and the less it is like a fluid. Tar is very viscous. Oil is somewhat less so. Water is less viscous still, and gasoline is extremely low viscosity, for liquids. Technically, air, being composed of gas, is lower viscosity yet.

I'm not sure what viscosity of a shampoo would mean as far as quality is concerned - the more a solution composed of soap and water is composed of water (i.e. the more diluted the soap), the more the fluid properties of the solution will resemble those of water, not the soap. However, this has nothing to do with the chemical solubility of the soap itself, what it can dissolve, and how readily. It also won't affect the chemical activity of the soap, i.e. whether the soap has any bad side effects on the skin of the person using it.