[dbieber]

Each data point is a bunch of features x_1, x_2, ..., x_n. You can make new features for your data points using whatever functions you like -- it doesn't matter if they're linear. Let's say we add two new features x_{n+1} = f(x_1, x_2) and x_{n+2} = g(x_2, x_3).

Now if we train a linear model on the new expanded set of features, it's linear in those features. It's not linear in the original data though, because of the new features that we introduced: x_{n+1} and x_{n+2}.