Where/what functions as a clock on a (say intel i3-7) microprocessor?
There will likely be a standard quartz resonator of some sort on the motherboard which will feed the CPU a reference frequency.  Inside the CPU, there is a device called a Phase Locked Loop (PLL) which is used to lock the output of a voltage controlled oscillator (VCO) into a well-defined relationship with the reference clock.  The output of the VCO will drive the clock distribution network on the chip.  

A quartz resonator is built from a small piece of quartz with electrodes deposited onto it along with an amplifier.  The crystal is cut to vibrate at a very specific frequency.  An applied voltage across the crystal causes it to deform via the piezoelectric effect.  Only signals at the correct frequency to make the crystal resonate will be passed through, making the crysal act like a very narrow bandpass filter.  The amplifier serves to amplify these oscillations to keep the crystal vibrating, as well as driving the signal out of the resonator.  

The VCO is simply a circuit that is designed to oscillate so that the frequency can be adjusted with an analog control voltage.  There are many ways to build a VCO depending on the process and frequency range.  One simple method is to simply vary the power supply voltage on a ring oscillator.  This will change the propagation delay of the inverters used to construct it, changing the frequency of oscillation.  Other methods involve utilizing the voltage variable capacitance of one or more varactor diodes.