See this great Stack Overflow answer.

I’ve also reproduced the whole thing below, and cleaned it up a bit.

## Explanation

I think that biases are almost always helpful. In effect, a bias value allows you to shift the activation function to the left or right, which may be critical for successful learning.

It might help to look at a simple example. Consider this 1-input, 1-output network that has no bias: The output of the network is computed by multiplying the input $x$ by the weight ($w_0$) and passing the result through some kind of activation function (e.g. a sigmoid function.)

Here is the function that this network computes, for various values of $w_0$: Changing the weight $w_0$ essentially changes the “steepness” of the sigmoid. That’s useful, but what if you wanted the network to output 0 when $x$ is 2? Just changing the steepness of the sigmoid won’t really work – you want to be able to shift the entire curve to the right.

That’s exactly what the bias allows you to do. If we add a bias to that network, like so: …then the output of the network becomes sig$(w_0x + w_1 \cdot 1.0)$. Here is what the output of the network looks like for various values of $w_1$. Having a weight of -5 for $w_1$ shifts the curve to the right, which allows us to have a network that outputs 0 when $x$ is 2.