Quick google search shows that China has its own Quartz mines, so I'm not sure if those are unsuitable for certain semiconductors or if the use of "world" here just means 
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i have no idea what an oscillator gizmo entails
Your computer's chips all have a clock rate, which controls how fast these circuits switches from positive to negative voltages. These clock rates are synchronised using an oscillator, often made of quartz.
By driving the clock rates from a single oscillator, multiple components can have different speeds but can stay in sync with each other, which is how we can transfer data from different components seamlessly.
An oscillator's output goes up and down. They can be sine waves (called harmonic oscillators), or any kind of wave. The ones used in digital circuitry make square waves.