Can anyone kindly explain to me what exactly is the cut-off line when facing a blank wall with your headlights on?

 

That is the line your headlights produce that separate the light from the dark. Used to avoid glairing towards oncoming traffic.

 

The cutoff line refers to the horizontal beam pattern your headlight output. Here's how a US DOT cutoff line look like on a wall:




Shown above is actually a modded RX330 projector I was testing on my IS. There's a step in the cutoff line. The lower step is designed so that on-coming traffic on the left will not get blinded.

 

A few of the newer cars that I've test driven. The cutoff line is a very low straight line without the split/step. I prefer the split which I have.