Basically, telomerase adds 6 nucleotides at a time to the end of a DNA primer. After it adds 6 nucleotides, it can either fall off or repeat its enzymatic cycle and add 6 more nucleotides.
Thus, when you look at the products of a telomerase reaction, you will see the unreacted primer at the very bottom of the gel, and above that band you will see a series of bands corresponding to primers that have been extended by the enzyme.
Although it's hard to tell how the authors measured the activity of the enzyme without looking at the paper, my guess is that they measured enzyme activity in each condition simply by quantifying the fraction of the DNA that got extended (i.e. the fraction of signal in all the bands except for the bottom band).