Yield stress is defined as the stress below which no flow occurs; literally behaves like a weak solid at rest and a liquid when yielded.
Many shear-thinning fluids can be considered to possess both liquid and solid like properties. At rest or near rest conditions, these fluids are able to form intermolecular or inter-particle networks as a result of polymer entanglements, particle association, or some other associated interaction. The presence of this network structure gives the material predominantly solid-like characteristics associated with elasticity. The strength of which is directly related to the inter-molecular or inter-particle forces (binding force) holding the network together, and hence its yield stress.
If an external stress is applied which is less than the yield stress, the material will deform elastically. However, when the external stress exceeds the yield stress, the network structure will collapse and the material will begin to flow as if it is a liquid.
Modern rheometers have many advantages over on early viscometer type indirect (extrapolated) yield stress measurements. The Kinexus rotational rheometer by NETZSCH gives several different methods to quantify yield stress dependent on the material type. Usually a direct yield stress measurement works well by increasing the stress applied to the sample directly, until the material flows.