Q:

What is purpose of black and white cables from LCD display?

When I disassembled laptop I noticed two wires from right part of display. What is purpose of them. They were connected to MAIN and AUX ports on some little board (which is under motherboard, so I couldn't see what it is).

A:

These are coaxial cables used to connect WiFi antennae to the WiFi card on the motherboard. The connectors in the photo appear to be U.FL and are commonly used for this purpose. They have nothing to do with the display itself, but laptop displays are a convenient location to mount the antennae: their environment is less noisy than right by the WiFi card. Furthermore, the antennae there can be oriented upright, which is often preferable, and the space around them is less dense because laptop displays stick up into the air. For these reasons, internal WiFi cards often have one to three leads like these going to various other parts of the machine.
When disassembled, treat these connectors with care. The cables carry a high frequency, noisy, analogue signal. Even tiny amounts of debris, e.g. oils from your fingertips, can have a strong negative effect on the wireless performance.

