A linear regression model implies that the outcome can be estimated by a linear combination of the predictors. This, of course, is not always the case, as features often exhibit nonlinear patterns.
Consider the following graph, where Y axis depends on X axis but the relationship displays an obvious quadratic pattern. Fitting a line (y = aX + b) as a prediction model of Y as a function of X does not work:
Some models and algorithms are able to naturally handle non-linearities, for example, tree-based models or support vector machines with non-linear kernels. Linear regression and SGD are not.
Transformations: One ...