The "often" is the key here - the way that linear models are built, especially compared to other types of models, are more likely to favor certain types of errors.... in this case, they are more likely to produce bias-type errors rather than variance-type. Another way of thinking about it is that the way that most linear models will give you broadly correct predictions overall, instead of specifically accurate or wildly inaccurate predictions. Obviously that's a super simplistic reading, but I've found an intuitive way to approach. Essentially - the way that linear models are constructed will lead them to predict more generally, instead of reflecting every type of twist and turn in the data. This is partially a function of the models themselves, and partially due to linear models being the first line of attack with smaller datasets.
If you think about the formula, one way to interpret is that the intercept generalizes the model's predictions. That being said, with enough variables and certain types of data, it's very possible to overtrain a linear model (which will tip it towards variance-type errors).
I like to think of the bias/variance tradeoff question as being one with three factors, instead of just the two in the title. I'll use the short definitions below (for more information, I've found wikipedia's article on the topic to be relatively clear):
- Bias - causing the types of errors frequently thought of as
"underfitting," high bias might generalize well at the cost of
capturing important nuances in the data
- Variance - causing the types of errors frequently thought of as "overfitting," high variance will capture most nuances in the
training data including noise that will reduce its likelihood of
generalizing well to future like datasets
- Data/Data Quality - While not usually included in the classic understanding of the tradeoff, data type and quality is integral to understanding why a certain model is tipping towards either the bias or variance sides of the tradeoff. This also includes any kinds of time effects or other quirks that in essence mean that a training/test split will not properly represent the model's future performance, especially as regards linear models.