"Facility" refers to the ease in which a drummer executes the notes and the dexterity displayed between the hands and hands/feet when playing.  Working through difficult patterns until they "feel good" increases your facility by adding to the list of skills and coordinations you've worked out.  Your muscles remember the stickings and beats you practice so the more patterns you work through the more fluid your playing will be and the more options available to you when presented with a new song, feel, or musical situation. 

Better facility will enable you to nail new stickings and beats faster, create more interesting and varied parts, and experience less "freeze-ups" when soloing or improvising.

Some things to discuss:

 - How to train your limbs, fingers to play effortlessly at a variety of tempos?

 - How to adjust for different volume levels?

 - How to work out the wrinkles in your playing? 
 - How to play what you hear without "freezing up"?