The Variation slider produces random variations of the filter look. Some visual aspects of many filters are determined randomly, for example the thickness and location of each 'vein' in the Organics filter, or the exact color of each tile in Decorative Tiles. These aspects cannot be controlled directly but they can be affected by Variation.
The exact numeric value of Variation doesn't matter much: you cannot predict the exact effect that a certain Variation value will have upon the filter look. You can think of Variation as a way to choose among 30000 predefined random appearances of the filter.
Variation is a global parameter – it is always present on the Settings tab in Filter Controls for any filter. However, if a filter was built without using randomizable components such as Perlin Noise or Bricks, the Variation slider is disabled.
To quickly browse through multiple Variation values, you can use the Randomizer on the Settings tab. To do this, set the Randomizer to Variation Only in Randomizer Settings, and click the Next Variant button to get new variations. You may also reduce the preview size by choosing View > Preview Size > Reduced from the menu to get the results quicker.
Technically, Variation is what programmers call a 'random seed', a value fed into all random number generators of all components in the filter combined with their own, 'local' Variation value. For details on how the global Variation affects the components, see How Variation Works.