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Let's say we have the model as y = mx instead of the y = mx + c. Here, the model is having constraint to train itself and find a line which passes only through the origin. Many times for the given data, it is impossible for the algorithm to fit the model so that it passes through the origin.
Let's give some freedom to the algorithm by changing the model as mx + c instead of mx, so that the model can find a line which fits the given data.
Bias is a constant which helps the model in a way that it can fit best for the given data. In other words, Bias is a constant which gives freedom to perform best.