An active filter is a type of analog electronic filter, distinguished by the use of one or more active components i.e. voltage amplifiers or buffer amplifiers. Typically this will be a vacuum tube, transistor or operational amplifier.
Active filters have two main advantages over passive filters. The first is that the amplifier powering the filter can be used to shape the filter's response, e.g., how quickly and how steeply it moves from its passband into its stopband. (To do this passively, one must use inductors, which tend to pick up surrounding electromagnetic signals and are often quite physically large.) The second is that the amplifier powering the filter can be used to buffer the filter from the electronic components it drives. This is often necessary so that they do not affect the filter's actions.