Linear models

A linear model predicts the target as a weighted sum of the features plus a bias (intercept):

Each weight $w_j$ says how much the prediction changes when feature $x_j$ increases by one unit, holding the others fixed. The bias $b$ is the prediction when all features are zero. Folding $b$ into $\mathbf{w}$ by adding a constant feature $x_0=1$ gives the compact form $\hat{y}={\mathbf{w}}^{\top }\mathbf{x}$.

'Linear' means linear in the parameters, not necessarily in the inputs. You can add $x^2$, $\log x$ or $x_1{x}_2$ as features and the model is still linear regression — which is how polynomial regression works.