A filter is an electrical device which removes parts of the spectrum of a signal passed through it. An equalizer permits passage of the entire spectrum, with level changes to some frequency bands. 
Filters usually act in a subtractive fashion and attenuate certain parts of the spectrum. Filters come in 5 types: low pass (high frequency attenuation), high pass (low frequency attenuation), band pass (atteneuates above and below a central portion), band reject (attenuates a central portion) & dip filters (very narrow band).
The compositional possibilities of filters are greatly increased when we consider modulating the parameters of the filter over time. (see low pass for sound example)
Filter parameters such as cut-off frequency, resonance, and amount of cut/boost are often controlled.  A simple low frequency oscillator (LFO) can be used or a more complex wave function defined and applied via MIDI or in software.  Filter parameters can be changed at relatively slow sub-audio rates or modulated at near-audio and audio frequencies. 
For a fuller description of filters see Equalization.