This is a calculation used to work out the effect of different filters on the exposure needed, but it’s largely fallen out of use with the arrival of digital cameras and especially mirrorless cameras. For example, a red filter, a contrast filter used in black and white photography, might have a filter factor of 3, so that you would measure the exposure without the filter attached, put on the filter and then increase the exposure by 3 stops. to compensate for the filter.
This was at a time when many in-camera meters had a different spectral response to film, so you could not get reliable exposure measurements with the filter attached. Indeed, many photographers of the time used hand held light meters or gauged exposure by eye, e.g. with the ‘Sunny 16’ rule, and simply transferred exposure measurements to the camera.
With digital cameras, it’s possible to take meaningful exposure measurements even with filters attached and, because you can see the captured image straight away, make any exposure adjustments and re-shoot if necessary.
The one instance where filter factors are still used is with strong neutral density filters such as the Lee Big Stopper, where the image is to dark for DSLR cameras to display it in the viewfinder even if the meter still gives a useful reading. Here, it’s normal to check the exposure (and framing) attach the filter, add the filter factor and shoot.
With mirrorless cameras this may not be necessary. The rear screen will adapt to even the dimmest image, as will modern exposure metering systems, so unless you’re shooting after dark, you may be able to compose and shoot even with a strong ND filter attached.