A filter is called such because it selects (”filters”) components of light, and either absorbs them or transmits them.  For instance, a yellow filter will absorb blue and transmit green and red light.  That is also the reason why it looks yellow.  A filter will absorb its complementary colour and transmit everything else.

Filters are/were commonly used in BW to achieve some contrast in the grey rendering of objects in colour. A panchromatic (all colour sensitive) BW film will render a red object and a green object -if they are of the same luminance- as equal shades of grey.  Using a red filter will let all the reflected red light in and block blues and greens- thus contrast separation is achieved by rendering the red object as light grey and the greens as dark grey in the monochrome picture.

To illustrate this principle, take a look at the following pictures:

1. The Original Scene as Seen in Colour:

2. Shot on BW, Without any Filter: Grey-rendering of hues (note the reds and the blues)

3. Through a Yellow Filter:  Yellow filters have sometimes been called “Cloud Filters”
 

4. Through an Orange Filter:  Contrast between coloured objects, particularly blue/green and red/orange is more pronounced.

5. Through a Deep Red Filter:  More dramatic skies, -darkened blue skies- darkened greens.

6. Through a Blue Filter: Mimicks the effect of the old colour-blind plates from the XIX century.

Note: Skies will darken only when they are truly clear and blue.  Hazy skies, cloudy and grey weather will not show the effect well.

Red and Orange, as well as Deep Yellow Filters will often render skins pallid and sometimes give a ghostly, drained-of-blood appearance to people and portraits.

Green filters are used to achieve a healthy, tanned look (green darkens reds) with people subjects outdoors. A green filter will also darken skies.