It depends on the color of your subject matter. Colored filters block the the colors opposite them on the color wheel (the light color wheel, RGB, not the pigment color wheel, RYB), causing them to underexpose, rendering them in darker tones than colors that aren't blocked.
If you photograph a subject that is green and red without a filter, then they may look tonally similar in a BW photo. If you use a red filter then the green parts of your subject will be underexposed; this will make the green parts look darker and the red parts look lighter. If you use a green filter the opposite occurs. Both filters increase the difference between your light and dark values, so both increase contrast. But if you use the red filter (or green filter) on an all green or red subject, then it will affect all of the subject the same, and contrast will remain the same.
A common use for colored filters in BW photography is to darken the tonal value of the sky so that there is increased contrast between the sky and clouds. BW film tends to be a little blue sensitive. This means that blue shows up as a lighter tone than we might expect. Many film manufacturers claim that they have corrected this (it used to be a bigger problem in the past), but it still seems to occur to me. A yellow filter is used to render a blue sky as a tone like we perceive it with our eyes. Orange increases the contrast between clouds and blue sky more than yellow, and red increases the contrast even more as red is opposite cyan (light blue) on the color wheel.
In another thread about BW filters, Motcon provided a good link to a page with BW filter info. Try to find it, or search for one of the many sites that provide a color wheel to look at. I think that this helps in understanding. Remember, you are looking for a light color wheel (red, green , and blue), not a pigment color wheel (red, yellow, and blue). Light mixes differently than paint or crayons.