How does the Kerr focusing effect leads modelocking?

I read about the Kerr effect in a medium like a Ti:sapphire focuses the Gaussian beam by acting like a virtual lens.

That is fine. But here is my confusion. Inside the cavity when the laser beam is focused how does it lead to pulses or how does it locks the modes?

Someone wrote "In short, Kerr-lens modelocking is based on the difference in loss (or gain) for continuous-wave (CW) and pulsed operation."

But I still don’t get the cause and effect relation here.

So there is a logical gap here in my thinking. I know what Kerr effect does to the intense Gaussian beam. I know(read) that this generates short pulses. But what is the relation between focusing and generating pulses here? Can this be explained intuitively using not much math?