High input impedance devices - induced noise sensitive
I like to give simplistic answers first. Then if more technical or details are needed, they can come later.
      - - - Imagine that a powerful external source of energy (magnetic, electromagnetic, nearby radio transmitter, whatever) had the ability to induce a current of 100uA (micro-amps) onto your signal leads. If you have a high input impedance, say 100 K ohms,  the induced voltage (noise) would be 10 volts (ohms law).  - - - If you had a low input inpedance (250 ohms common in 4-20mA system), the 100uA would result in .025 volts (25mV noise) impressed upon your signal. 

Further, 100uA is only 2.5% of your lowest signal of 4mA in 4-20mA system.