The Evanescent field is a portion of the light that hits the interface between the core and cladding and is available to interact with anything that is outside the core.
In the “measurand picture”, the measurand could be a liquid or a gas for example.
This can be used as a sensor. In this case, light in launched into the core of the fiber. If the measurand is not absorbing to this light, the signal will be high at the output. If the measurand is absorbing, it will absorb some of the light in the evanescent field and the output signal from the fiber will be decreased.
Hope that makes sense.