A hard threshold is when we have a discontinuous change when the output exceeds a fixed threshold value, for example changing from 0 to 1 when an input temperature exceeds 373.2. Hard thresholds are easy to implement, but may lead to fragile models and cam be hard to learn. For this reason many algorithms, notably backpropagation use a soft threshold function such as a sigmoid.
Used on Chap. 9: page 192
Step threshold function -- a hard threshold