According to The Discoverers by Boorstin, there was no reliable way of keeping track of minutes and seconds throughout the day until the invention of reliable clocks a few hundred years ago. Prior to this, people had to use sundials, which could only keep track of hours and only during the day, and hourglasses, which had to be reset manually.
How did this change human life and culture?
Boorstin! Loved that book.
James Burke (and others) tied the invention and widespread availability of clocks with work. There's a fun episode of Connections based around clocks.
Some of the first clocks in Europe were used by monks who needed to keep track of times to pray. He rebuilds a water clock in that one based on a fragmentary 11th century manuscript found in a monastery in the Pyrenees. (It's around 16 minutes into that video.) It's designed to wake you up for nocturns, the prayers said in the middle of the night.
Having a tool to wake you up means you don't have to wait for the sun any more. You don't have to (or, more darkly, aren't able to) sleep according to your body's needs. You can get up and do things.
By the way, those monastic alarm clocks were only about as old as Su Song's clock tower, which was a bit more impressive as a construction - it was 40 feet tall and built of bronze between 1088 and 1094 CE.
Unfortunately, it was disassembled by an invading army about a century later and carted off to Beijing, where no one could figure out how to put it back together again. Only recently, in the 1990s, were some folks able to follow Su Song's book on clocks, figure out the stuff he didn't include (to keep folks from copying his ideas) and rebuild the clock at Taiwan's National Museum of Natural Science.
Song based his design on earlier Chinese water clock designs, one of which used mercury (which wouldn't freeze in winter).
One major use was being able to calculate one's longitude on the earth, which made a lot of exploration and accurate mapping possible.