It is referring to the effectiveness of the fermentation in the yeast consuming sugars. Yeast can typically attenuate up to 85% of the sugars with a normal range of 65%-85%. A well attenuated finished refers to a dryer finish without residual sugar sweetness. That comes from a well attenuated fermentation on the 85% side.
attenuation is determined by measuring the gravity before and after fermentation. the formula is [(OG-FG)/(OG-1)] x 100. So, for a 1.050 beer that finished at 1.010 you have 1.05-1.01=.4, .4/.5=.8, .8*100= 80%. This would be on the well attenuated side and would be typical for a German Altbier.
The choice of yeasts is very important as you need one that is a high attenuating strain and one that does so in cool temps.