What does the vertical sync cable used for？

It offers the clock signal to drive the vertical axis. Here's a good write up: Vertical Sync.

As LCD's have gotten larger, the need to deal with movement of the image across the screen to prevent tearing or blurring was needed. One of first methods was to drive a vertical sync and the next was increase the refresh rate (60, 120 and commonly now 256 KHz).

As the screens are even getting larger and the density of the pixels deeper other methods are now being used. Take a look at the iMac 5K teardown to get an idea on how its being done.