The difference between the usual color and monochrome  (“black and white”) cameras is an additional layer of small color filters, mostly arranged in the so-called “Bayer pattern” (patented in 1976 by Bruce E. Bayer, employee of Eastman Kodak).

Bayer Pattern on image sensor, (C) Wikipedia

In an ideal world, a lens would map any (arbitrarily small) point on the object to an (arbitrarily small) point on the sensor, and pixel could be supported, regardless of their size.

Unfortunately, by physical laws, it is only possible to illuminate little light disks(=”Airy disks”). The specified number of megapixels for a lens is a rough measure of the size of  these disks (we are talking in terms of micrometers here). The more megapixels, the smaller the disks.

In order for the image on a monochrome sensor to be in focus, the disks must fit in the footprint of one  pixel.
On a color sensor with “Bayer pattern”  there are red pixels only in every other column and row. Here, disks of light that fit in a single pixel, may even be undesirable:

Sample for color moiré (click to enlarge) , (c)Wikipedia

The disks should be so large, that one red, one blue and two green pixels are always covered, e.g. 2×2 pixels in size. This means that the lens, in  comparison to a lens for a monochrome application/camera, can and maybe even should have a reduced resolution. To avoid the color moiré we can use a lens with a lower resolution, as stated above, or an (expensive!) so called “OLPF” (=”Optical Low Pass Filter”) that ensures a guaranteed minimum blur of 2 pixels. Such filters are required when customers request videoconferencing and want to avoid color moiré.