A measurement chain comprises all components that convert a physical quantity into a usable measured value.
It consists of a sensor (e.g., strain gauge), a measurement amplifier or electronics for signal conditioning, and software for evaluation and display.
Cables, connectors, and filters are also part of it, as they influence the signal and thus the measurement result.
In short: The measurement chain includes everything involved in the signal path that can alter the measurement result, from the acquisition of the quantity to the display of the measured value.