What is the pixel clock setting on my monitor actually doing?

The pixel clock adjusts how wide the input pixels are. VGA is an analog input, there are no clear-cut boundaries between pixels and the monitor must guess.

If the clock setting gets misadjusted, your display gets blurry and that’s probably why it no longer causes interference.

To adjust the clock and phase settings properly, view a pixel checkerboard on your screen and use the “Auto” option in your monitor menus.

Also, have you considered connecting your screen via DVI?

I am no expert in this, but from what I could find out, the pixel clock (or dot clock) is the speed at which the pixels are transmitted such that a full frame of pixels fits within one refresh cycle. For example, a VGA's pixel clock set to 25 MHz (corresponding to 25 million pixels per second) is just enough to display a resolution of 640x480 at 60 Hz (note the active display is only a part of the frame). Most higher resolution video can therefore use a wide range of dot clocks, well above 25 MHz, with the current range allowing enough bandwidth to easily exceed 1600x1200 at a 100 Hz and beyond.

The best way to figure this out is to search for the video standard you're trying to do, or look at the datasheet for the screen you are trying to drive and set the correct pixel clock as per your needs.