But the meaning of the word is broader: A bias is any predictable error that inclines your judgment in a particular direction. For instance, we speak of bias when forecasts of sales are consistently optimistic or investment decisions overly cautious.
To see the difference between bias and noise, consider your bathroom scale. If on average the readings it gives are too high (or too low), the scale is biased. If it shows different readings when you step on it several times in quick succession, the scale is noisy. (Cheap scales are likely to be both biased and noisy.) While bias is the average of errors, noise is their variability.