While quartz measures the passage of time in micro-moments that are imperceptible to humans, liquid crystal helps depict the passage of time on the display in ways we can easily comprehend.
We mentioned earlier that liquid crystals have optic properties that make them a favored component of LCD screens. Liquid crystal substances are classified on a spectrum between solid and liquid, depending on their individual characteristics. The most common type of display used for LCD screens on a digital watch is called a twisted nematic (TN) display. The molecules that make up the liquid crystal in this display are arranged in a twisted, spiral shape. But the chemicals can be untwisted by applying an outside force -- like an electrical pulse -- which will affect the light passing through them.
An LCD on a watch essentially sandwiches liquid crystal chemicals between two electrically conducting glass plates, with polarization filters attached to each plate and oriented 90 degrees to one another. The liquid crystal molecules naturally run parallel to the polarization filter, allowing the illumination from ambient light to reflect off of a mirror placed underneath the polarizer -- this is what gives the LCD its silver appearance. However, applying an electric charge to the liquid crystals changes their molecules' orientation to run perpendicular to the polarization filter, and the filter absorbs all of the light, leaving black cells on the display.
When the integrated circuit releases those electric pulses after every second, minute, hour and other intervals measured by the quartz oscillator, it communicates with the LCD to turn parts of the LCD on and off. The LCD is divided into a series of seven- or 14-segment sections, and each seven-segment section conveys a numeral zero through nine. The combination of sections can reveal the passage of time from 12:15 to 12:16, for example, or 1:00 to 2:00. (By virtue of having more cells, 14-segment sections can reveal letters as well as numbers.)
As you can see, quartz and liquid crystal are very different substances serving very different purposes when it comes to keeping time. But without both of them working together, we'd probably be running late.