The text that is above the figure is from my textbook and i am having difficulty to understand what it is trying to say because it's not in detail!! why only remove high frequency and prevent low frequency using capacitor on ground G2? also What is the difference between both the grounds?
The critical reason for the low frequency blocking capacitor is avoiding large DC currents to flow. In any practical application, "ground" is only at zero potential in a very small region; the "ground" potential can vary across a circuit board, equipment chassis, or or larger assembly of equipment (telecom, AC power, building) due to current flow and non-zero resistance. Thus, connecting the shield of the twisted pair to both the sensor and the amplifier could cause such current flow between G1 and G2, since they are different "grounds." Depending on the reasons for the ground loop and the common grounding conductor, it is possible for a little interference to thousands of amps to flow because the two grounds otherwise have a high-impedance connection. This depends on the equipment and other electromagnetic situation at each end of the sensor wire connection.
The use of a capacitor means that high frequency noise/EMI is conducted away from the sensitive in-amp nodes because the capacitor connects the two grounds only at high frequency (where the capacitor presents a low impedance). This also reduces the buildup of large potential on the shield relative to the amplifier due to this high frequency noise because they are conducted, through the capacitor, to the ground of the amplifier.
Your circuit shows two remote grounds; one at the sending end and one at the receiving end. Those two grounds will not be at the same potential - imagine a bunch of plant machinery at one end and another bunch of plant machinery at the other end. The Plant machinery can create significant ground currents and the relative potential difference between the two ends is just not constant.
However, neither is it going to be hundreds of kHz - it's going to be mainly from 50 Hz to a few hundred Hz and maybe a few kHz. But, if you put a wire between those two points what would happen - you'd get ground currents travelling along the screen of the cable. Those ground currents may be "low" in frequency but they could still induce "volts" in the signal wires. Yes, it'll be common mode noise but it could still upset things and severely degrade the signal at the receiving end.
Worst case scenario - it could damage circuits.
Personally I'd ground the screen at the receiver end and leave it open circuit at the send end and if it doesn't look good I'd put the capacitor at the sending end. Personally I think they got there diagram the wrong way round.