What exactly does "Mouse filter" do?

[Azureth]

I see it a lot in FPS games, what exactly does it do? And would you recommend using it?

 

[Ron FTL]

From here

Mouse filter smoothes out mouse movement. This may sound like a good idea, but it is best left unchecked. Enabling it will only distort your aim, moving your crosshair slightly off cue from where you want it. If turned on, Counter-Strike will calculate all your mouse movements over the last two frames to find an average and attempt to give you a more fluid feel. This means using older data to move your mouse instead of the most up to date information. Theoretically, with mouse filter off, you could also receive a slight FPS boost on lower end systems.

Personally I would leave it off. I tried it a long time ago and didnt notice any significant difference.
I have left mine off for the past few years.

 

[aeonrevolution]

If you're playing anything somewhat competitively, do yourself a favor and turn it off.

If you're just playing BioShock or something then go ahead and fiddle with it and see which one feels better.