A filter factor is highlighted on many filters as a multiple (or x). It’s simply the amount you need to increase the exposure by to compensate for light absorbed by the particular filter being used.
x2 is a one stop increase
x4 is two stops
x8 is three stops
x16 is four stops
If, for example, you have a x4 orange filter on the lens, the exposure has to be increased by four times – that is two full f/stops or shutter speed increments.
Lets say you have an exposure of f/5.6 (aperture) and 1/125sec (shutter speed) and add the x4 filter. You would either have to adjust the aperture two stops to f/2.8 or the shutter speed two stops to 1/30sec or both one stop so the exposure would be f/4 at 1/60sec.
Fortunately with modern through-the-lens (TTL) metering and automatic cameras the filter factor is taken care of, but you need to make the necessary adjustments when using manual cameras or manual exposure with flash.
To make things a little more complicated, some filters, such as the polariser, have variable exposure factors as you rotate the filter, and others have incremental factors such as 1.3x which makes it hard to adjust if you have an older camera with only full stop increments.