Taken from
https://www.thefreedictionary.com/bias
Verb 1. bias - influence in an unfair way; "you are biasing my choice by telling me yours"
prejudice, prepossess - influence (somebody's) opinion in advance
handicap - attempt to forecast the winner (especially in a horse race) and assign odds for or against a contestant
2. bias - cause to be biased
predetermine
prejudice, prepossess - influence (somebody's) opinion in advance
slant, weight, angle - present with a bias; "He biased his presentation so as to please the share holders"
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Biasing in the electrical or electronic sense is much similar to the English meaning of the word 'bias' - to influence in an unfair way. A common example is the transistor which we use to amplify an AC signal. To make the transisitor work, we will need to apply a DC to turn it on. Biasing in this sense is to use a DC to influence the AC signal such that it is prejudiced into the region of operation of the transistor.
One commonly overlooked example is the polarised electrolytic capacitor. If we just pass an AC through, one half of the cycle will be distorted because the polarised capacitor works only for one direction of current flow. So this AC signal should also be influenced in a way such that it becomes unbalanced with a DC offset such that the AC signal can pass through the capacitor without distortion.
An example cited by flatulent is a classical example of biasing with another AC signal. To overcome magnetic hysteresis, analog tape heads for recording are biased with a high frequency AC signal. So the original audio signal is added with a high frequency signal that is used to overcome the hysteresis while the audio signal gets recorded onto the tape.