A filter is a color "lens" that goes over a camera lens to alter the light usually the color. Some filters are "pink" to correct for flourescent lights and some are blue to correct for indoor incandescent lights.
A filter for painting has the same effect. Applied it is like a wash, basically very thin paint. It is applied such that the base coat shows through but the filter alters the color and blends in the base coat where there are different contrasting colors underneath to provide a smooth transition.
It's kinda hard to explain, but picture having colored transparent cellophane and putting it over things you want to view. That acts like a filter and think about paint being applied to have this effect. The paint must be very thin so it doesn't cover the color underneath it.