The squatting is a readiness for breeding posture. It merely is one signal of sexual maturity. The egg is not going to pop out because of the squat. The pullet squats in your presence because you represent a big creature, possibly a rooster, and she is being submissive. I usually just rub my foot on their backs for a second or two and they seem to love it. They fluff their feathers and walk off proudly, assuming they've just been bred.
The pullets begin by dropping little, thin eggs, that often are rubbery or thin shelled. Within a week, their reproductive system comes up to speed and the genuine eggs begin to be laid.