Metric time has a hundred seconds to a minute, a hundred minutes to an hour, ten hours to a day, and so on. Metric time is great for measuring time and doing calculations on it, but poor for making decisions on when to go to bed.
Unfortunately, the below clock follows your local UTC rather than TAI. A clock following TAI would be completely linear, with none of that leap second nonsense.
Solar time follows the sun. The simplest example is a sundial. Solar time is great for planning human events, such as when to get up in the morning.