In signal processing the complete or partial suppression of some aspect of the signal. Or selecting a subset of some set of data.
Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal. Most often, this means removing some frequencies and not others in order to suppress interfering signals and reduce background noise. However, filters do not exclusively act in the frequency domain; especially in the field of image processing many other targets for filtering exist.
A less abstract application of filtering is when you have a set of data that needs to be refined according to a predetermined filter (which could be specified by a user or constructed programmatically). Applying the filter reduces the set of data, eliminating that which falls outside the bounds of the filter - the resulting filtered set of data could then be shown in the user interface.