<p>Graphics and audio editing and processing software often contain functions called "High-Pass Filter" and "Low-Pass Filter".  Exactly what do these do, and what are the algorithms for implementing them?</p>

Wikipedia:
High-pass filter
Low-pass filter
Band-pass filter
These "high", "low", and "band" terms refer to
frequencies
. In high-pass, you try to remove low frequencies. In low-pass, you try to remove high. In band pass, you only allow a continuous frequency range to remain.
Choosing the cut-off frequency depends upon your application. Coding these filters can either be done by simulating RC circuits or by playing around with Fourier transforms of your time-based data. See the wikipedia articles for code examples.