What is the use case of Pixels?

Depends on your imagination. The main idea back at 0.14 version of Factorio to have the way to notify player through the dynamic symbols/pictures on the map. For example - you can use Pixels to notify you when the Coal storage is low. If the coal is low - Pixels turns red, which is immediately shown on the map. In the latest versions of Factorio Pixels could be combined with the Programmable Speaker to notify you directly. Also it could be used as a silent notifier - a set of a digits that is updated according to the storage value, or, maybe, the batteries capacity which will show you the needed information on the map with no delay in real-time.

How to use Pixels?

Pretty much the same as you use Colored Lamps in "vanilla" Factorio. Just place Pixel (in-game name is "Light Emitting Diode, Lightning Technology), connect it to the circuit and adjust circuit conditions so it will react on Anything that is more that 1. Then you have to give it a colored signal from circuit. If you don't know how to use circuits - refer to Wiki Pages.

How it works?

It works by just placing the pre-defined tile with pre-defined map color under the Pixel. So the mod dynamically detect the changes on the circuit and updates the tiles under Pixels. It is not possible to update more then 1500 Pixels at a time because they are all updated during 1 tick of the game. This problem will be fixed in the future releases by checking it chunk wise. For now it is not possible due to desync problems.

Can I change the tile that is placed under the Pixel?

Yes you can. Just open the Mod Settings in the Factorio Main Menu and choose the Tile Under Pixel drop down option. For now there's only 2 tile types available - Concrete (default) and Green Grass. I will update the list in future releases.