Types of variation
The ideas of signal and noise correspond to explained and unexplained variation in a variable, X.
In some data sets, none of the variation in X can be explained in terms of other variables that have been recorded. In other data sets, some of the variation in X can be explained in terms of other variables whose values are available, but part of its variation remains unexplained.
A statistical analysis often separates and describes these two components of the variation. Both provide useful information.