Telescope filters divide into the ones that work by physics and the ones that work by hope, and the difference is easy to state: a filter can only remove light, never add it. This page starts with the two most commonly bought and says plainly what each does.
Moon filters, which are about comfort
A full moon in a 200mm telescope is uncomfortably bright and leaves an afterimage that ruins your dark adaptation. A neutral density moon filter dims it, which makes extended lunar observing pleasant. It adds no detail and it does not need to: the moon has plenty of contrast. A variable polarising filter does the same job adjustably and is better value.
Light pollution filters, which work on emission objects only
A broadband light pollution filter blocks the wavelengths of sodium and mercury street lighting while passing those of emission nebulae. Against those targets it genuinely improves contrast. Against galaxies and star clusters, which emit across the whole spectrum, it dims the object as much as the sky and helps nothing. Broad spectrum LED street lighting has reduced how much these filters can do.
What no filter can do
No filter makes a telescope gather more light, and none improves a galaxy under a bright sky. Sold as a general improvement they disappoint; sold as narrowband tools for emission nebulae they are among the most effective accessories available. The honest question before buying is which of your targets emits at specific wavelengths.
Questions people ask about light pollution filter
Do moon filters work?
Yes, for comfort. They dim a bright moon so it is pleasant to observe and your dark adaptation survives, and they add no detail because none is needed.
Do light pollution filters actually work?
On emission nebulae, clearly yes. On galaxies and star clusters, no: those emit across the spectrum, so the filter dims the target as much as the sky.
What filters should a beginner buy?
None at first. A moon filter if the full moon is uncomfortable, and a narrowband filter later if nebulae become your interest.