Any machine learning model is trained based on certain assumptions. In general, these assumptions are the simplistic approximations of some real-world phenomena. These assumptions simplify the actual relationships between features and their characteristics and make a model easier to train. More assumptions means more bias. So, while training a model, more simplistic assumptions = high bias, and realistic assumptions that are more representative of actual phenomena = low bias.
In linear regression, the non-linearity of the features is ignored and they are approximated as linear variables. So, linear regression models are inherently vulnerable to exhibiting high bias.