The 10,000 year clock is designed to measure time in years and centuries, rather than minutes and seconds. It will tick once a year. The century hand will advance, you guessed it, once a century, and the cuckoo will emerge once a millennium. The idea is to give us a greater sense of the impact of our decisions, and to think about long-term consequences of what we do.
According to Bezos' tweet, the clock will be powered by day and night thermal cycles and synchronized at solar noon. The team just finished drilling a 500 foot deep vertical shaft for the clock. You can see a video about the process embedded in Bezos' tweet below. (His connection to the project: The clock is being installed on a plot of land that he owns in Texas.)