What is exactly meant with linear relations and non-linear relations in the data? I often read the statement that for example logistic regression is a good model for easy understanding the linear relations in the data. While for example classification trees are better to understand non-linearities. I'm struggling a little bit with the term "linear relations in the data". I know that the logistic regression model is linear in the parameters but non-linear in the covariates / features. 
How is this linear relations in the data to understand? The following sources / papers used the terms as described above:


*

*Link1 On page 40 (3.4.1); The author states: 

The logistic regression models lend themselves to easy understanding
  the linear relations in the data


*Link2 On page 6; The author states: 

Machine learning offers a set of tools that can usefully summarize
  various sorts of nonlinear relationships in the data

 A: While no one can read the authors' minds and tell exactly what they meant, linear relationships are usually regarded as easy to understand because there are relatively few things to look at in the output and the relationships are constant across different levels of the independent variable.  E.g. we might find 
$logit(y) = b_0  + b_1x_1 $
which would mean that the effect of the x variable on the logit is the same at all levels of x1. 
The second quote is vaguer, but, for instance, output from a spline regression is often a lot more complex and the relationship between X and Y varies at different levels of X.
However, the advantages of these more complex models are that they make fewer assumptions and often give a better fit. 
A: When logistic regression is used as part of a classification problem, the data space is separated by a straight line (resp. Hyperplane in dimensions above 2). Subjects are assigned to a class according to which side of the Hyperplane they are on. In that sense, the classifier is linear.
Note: quick clarification. If you have $n$ features for each subject, then each subject can be mapped to a point in $R^n$.
Classification trees also split the sample space into regions but the boundary would not be linear. You would get a bunch of box like regions, I believe.
Neural networks and kernel classifieds allow more complex divisions of the sample space.
