[Argus25]

Basically, the horizontal scan oscillator and the vertical scan oscillator (in the absence of separated sync pulses from the received signal) are "free running"

These scan oscillators generate the basic waveforms (similar but not exactly sawtooth in shape) that drive the horizontal power output stage and H yoke coils, and the vertical power output stage and V yoke coils. The result is, as you now know, being a H and V sawtooth current in the yoke coils to deflect the electron beam. (In electrostatic sets it is a sawtooth voltage driving deflecting plates not sawtooth current). You will learn later why the actual drive voltages from these oscillators are not exactly sawtooth in shape, they are a shape known as trapezoidal, the effect of this shape results in actual sawtooth current occurring by the power output stages that drive the deflection yoke, which is what is needed for a perfect scan.

So when the picture signal (often called the composite video signal as it is sync & picture information) comes in and appears at the output of the video detector stage, the syncs are separated off, as H and V syncs by sync separator circuits.

These sync pulses are used to "Lock" the free running H & V oscillators so that the picture information you see on the screen starts in the correct place on each scanning line and the start of each field (two fields make a whole frame). In each case there is a rapid fly back.

(You are probably now aware that the image you see on the screen is the result of the picture information part of the composite video signal modulating the intensity of the picture tube's scanning beam. This video signal voltage is applied to either the grid or the cathode of the picture tube depending on the set design)

In the case of the vertical sync pulse, it is really a small voltage blip that is injected into the V oscillator circuit. Normally, when the V oscillator is set to run a tad slower than the sync rate, the blip triggers the oscillator just before it is about to fly back anyway. At that point the oscillator is more sensitive to the sync pulse. This is how the oscillator can be "locked" to the sync pulse.

If the received signal is weak and the V sync too low to lock the V scan oscillator, you can set the V hold control (Vertical oscillator frequency control) so that you see the wide horizontal bar between the frames rolling upward a little in this unsyncronized state. That means the oscillator is running, in the absence of sync, just a tad slower than the vertical sync frequency, which is about where the control should be set.

In very old sets, the H sync was done in the same way, but in this case line by line and the H sync pulse triggered fly back of the line (H) oscillator, just before it would have flown back anyway. This system though was pretty sensitive to noise pulses causing a tearing look of groups of lines.

However as time went by the H sync and oscillator circuits became more complicated and instead the H scan oscillator became an oscillator controlled by a DC voltage rather than synchronised by a discrete sync pulse. Then a circuit using a pair of diodes compared the phase of the oscillator output (often sampled from the H output circuit) and the incoming H sync, to create a DC error voltage to control the H oscillator frequency.

On these TV sets sometimes said to have AFC (automatic frequency control) when you turn the H hold control, once the picture has locked up, it then stays in lock over a large range of H hold control motion, and the picture appears to move left & right in the scanning raster. So the H Hold control then acts like a defacto H picture centering control, but you can only push that so far before it "drops out of lock" and the picture tilts over on its side to become an array of diagonal bars.
This type of circuit generally is known as a "Phased Lock Loop"

It will become much clearer, keep working through the book, and once you have gone through it once, go back to the beginning and do it again and it makes more sense the second time etc. But you are obviously picking it up very quickly.