The difference between the expected value of a parameter estimator & the true value of the parameter. Do NOT use this tag to refer to the [bias-term] / [bias-node] (ie the [intercept]).

Bias, in a statistical framework, means that an estimate of a parameter has an expected value that is not equal to the actual parameter value. The bias of an estimator can be evaluated with the mean squared error: $$MSE(\widehat{\theta}) = E[(\widehat{\theta} - \theta)^2]$$ which can be decomposed into the sum of the squared bias and the variance of an estimator.

One common example of using a biased estimator is ridge regression; ridge regression can be useful when there is collinearity. The estimators are biased (unlike OLS estimates) but have much lower variance.