A data logger is an electronic device that automatically measures voltage at specified time intervals and stores it in memory. typically you'd read it out into a spreadsheet after the experiment was over and do your analysis & graphing that way.
The rectangle in the circuit diagram is supposed to be the potentiometer. A potentiometer is a 3 terminal variable resistor, you can put the two end terminals of the track across a potential difference and adjust the wiper position to get any potential inbetween those two on the third terminal.