What does "correlation" mean in signal processing?
What it usually means:  


  "correlation, In statistics, the degree of association between two random variables. The correlation between the graphs of two data sets is the degree to which they resemble each other. However, correlation is not the same as causation, and even a very close correlation may be no more than a coincidence. Mathematically, a correlation is expressed by a correlation coefficient that ranges from −1 (never occur together), through 0 (absolutely independent), to 1 (always occur together)."  


(from Encyclopedia Brittanica)  

Uncorrelated white noise means that no two points in the noise's time domain are associated with each other. You can't predict any noise value at any other time from the noise level at time \$t\$. The correlation coefficient is 0.
Even if you know the noise signal over an eternal time, except for that one picosecond, all this information can't help you to fill in that picosecond's level. That's zero correlation.  

Correlation within the signal itself is called autocorrelation.