A sensor has a certain number of light gathering pixels, and typically the higher the number of pixels, the higher the image’s resolution. This absolute resolution is directly related to much white light or luminance is reaching it.
Colour in an image is created through a demosaicing process that interprets the light reaching the sensor through a colour array placed between the light source and the sensor.
The colour array has a pattern of coloured pixel-sized pieces of glass that allow only one colour to reach each individual pixel on the sensor sensor, usually they are either red, blue or green. A demosaicing algorithm, know as colour reconstruction estimates what the original colours were and then blends this information together to create a colour image.
Bayer Filter Array
Bayer filter arrays are found in most cameras, Fujifilm X cameras being one of the few exceptions. A bayer filter has a two by two array with one red, one blue and two green filters. One of the problems with a bayer filter is the demosaicing algorithm working with this very repetitive pattern can result in the risk of moire. You can see moire in the image below. To prevent this, camera manufacturers would reduce the actual resolution of the image using an anti-aliasing filter. As sensor resolution increased camera manufactures began removing the anti-alias filters in favour of better resolution, however this remove the problem. When moire does occur post processing is one method of removing it, in otherwords the defocusing or slight blurring is done in post processing.

X-Tran Filter Array
An X-tran filter array placed over the sensor has a six by six pattern instead of the two by two pattern of the Bayer filter. So it will have a more complex demosaicing algorithm than the Bayer array. The resolution from cameras will be the same as a similar sensor that does not use an anti-alias filter, however the colour resolution will be less. Colour simplification is not necessarily a negative thing as it is often used used in post processing to enhance an image. As the resolution is not impacted it becomes a matter of personal taste. All cameras use a different processing engine which will result in a different look to its JPGs or RAW files, and in some instances this influences photographers camera choices.

RGBW Filter Array
A RGBW filter array uses a six by six array like the X-Tran array but rather additional green filters it uses white. In otherwords there is no filter the open pixel allows more light to pass through the array onto the sensor. The colours for the white filter are estimated by looking at the surrounding coloured filters. The net result is superior performance in low-light situations. This can be done in a number of ways as illustrated in the image below.

References
- X-Trans: The Promise and the Problem, Jonathan Moore Liles.
- Joint learning of RGBW color filter arrays and demosaicking, Chenyan Bai Faqi Liu and Jia Li
- Color reproduction pipeline for an RGBW color filter array sensor, Wonseok Choi, Hyun Sang Park, and Chong-Min Kyung