What is meant by counts of noise in this context?
When talking about ADCs, we often refer to the smallest change in the output as a "count". 

16 counts of noise means the numerical value of the digital output value could change by 16 (or maybe by 8 in either direction, or maybe by 16 on average but possibly much more). 

But it feels awkward to just say "change by 16" without saying 16 of what. So we say 16 counts, or sometimes 16 lsb's.