Tbc
Cutting through the engineering gobbledygook...
The video has a certain resolution, say 480i (720 x 480) , which means the image consists of 480 horizontal lines and 720 vertical lines. The display needs to know when it has received a full line and should drop down to the next line to continue drawing the image. Likewise, it needs to know when it has finished the entire image so it can go back to the top and start the process over. The analog signal contains 'sync pulses' and they tell the display where lines start and end.
That is the figure in the article that shows 64 microsecond pulses to indicate the edges of the lines. If noise distorts the sync pulses or the source device, like a VCR, cannot output the signal with stable timing it becomes difficult for the display to know when lines start and end and that results in visible artifacts.
So instead of the display having to 'look' for the pulses in real time, the TBC identifies the timing, buffers the signal, and then outputs it with the exact timing to the display so the display can easily identify the transitions; ie the sync pulses will be more regular and always be at 64 us (as in that example) as opposed to possibly 64, 63, 65, 64 etc without correction.