For example, red is the complementary (opposite) colour to blue, so by using a red filter, you block most of the light from a blue sky. As a result, blue skies come out almost black to produce a dramatic, high-contrast image where any clouds stand out vividly.
This is fine for dramatic, high-contrast images, but a little too strong for most landscape photographs. Here, photographers often prefer a yellow filter, which still darkens blue skies, but not quite as much. At the same time, because vegetation contains a high proportion of yellow, a yellow filter lightens grass, trees and other greenery.
It's also possible to get yellow/green filters which are designed to enhance greenery just that little bit more, or orange filters which have an effect somewhere between yellow and red, so that you get more dramatic skies without the excessive contrast of a red filter.
Contrast filters are used less often with digital cameras because it's easier to shoot in colour and then choose a filter effect digitally when you convert it to black and white. You can do this using the Channel Mixer in Photoshop, for example, or with a dedicated black and white plug-in like Nik Silver Efex Pro 2.