Filters are and always have been an essential part of dance music, and many other forms of music for that matter. They can be used as a creative tool to increase and/or decrease energy on a certain element by sweeping through the frequencies of a sound, and, can also be used as a technical tool for removing unwanted frequencies from a sound in a mix.
The most common use for a filter from a mixing point of view, would be to high-pass (cut low frequencies) from most of the elements in the mix, typically to make room for the kick and bass. This is commonly done through use of EQ. Filters are essentially part of the EQ family, the only difference being that filters are generally meant for only cutting frequencies from the sound, whereas EQ is used to shape the tone of a sound using a combination of filter shelf and/or bell shaped slopes to boost or cut a specific range of frequencies from the sound.
There are 4 types of filters commonly found on your basic stock filter device. Low-pass, high-pass, band-pass and notch.
Low-pass filters allow low frequencies to pass through while gradually cutting the high frequencies content from a sound.
High-pass filters do the opposite, allowing high frequencies to pass through while gradually cutting the low frequencies.
Band-pass filters are basically low and high-pass filters, used together. This allows for a certain range of frequencies to come through while filtering out the audio above and below the selected frequency.
Notch filters do the opposite, allowing you to surgically remove very specific frequencies from a sound.
One of the main areas to pay attention to aside from the filters frequency cutoff control, is the resonance or "Q". This allows you to boost or reduce the frequency around the point where you would set the filters cut off frequency. The most common example of this taking effect would be the classic "filter sweep" sound, heard on white noise generated from a synth oscillator. This is commonly used as an effect during a tracks transitions from A to B sections, or in a tracks buildups and breakdowns. The higher the resonance, the more noticeable the filter sweep will sound. And the more narrow the resonance is set to, the more ringing or feedback you will hear from the sound, at a specific frequency. Using narrow q values are also used in equalization when searching from problematic frequencies in a mix.