Filters are everywhere.
There are all kinds - linear and non linear. Digital linear filters are an important computational tool in geophyscis. The discussion of linear filters is probably best motivated by recognizing the frequent need for 'data smoothing'. Give a 6 year old child the task of smoothing a time series, and you will get a nice crayon line which removes objectionable bumps and wiggles from your time series. To the 6 year old, the task of drawing a smooth line constitutes computing a 'local average' of the time series, which can be summarized via a digital filter equation.