Why is the day slowly getting longer?

The Moon raises tides in the oceans, and the Earth rotates underneath those bulges, dragging them slightly ahead of the Moon. Friction from that dragging acts as a brake on the Earth's spin, and the same interaction hands the lost momentum to the Moon, pushing it about 3.8 centimetres further away each year. We know the figure precisely because Apollo astronauts left mirrors on the surface and lasers have been bounced off them ever since.

The rate is around 1.8 milliseconds per century, which sounds negligible and is not, over deep time. Coral and shellfish lay down daily and annual growth bands, and fossils from the Devonian, some 400 million years ago, record roughly 400 days in a year - the year was the same length, and the days were about 22 hours long.

Run it forward and the Earth eventually becomes tidally locked to the Moon, each showing the other one face permanently, with a day and a month both about 47 of our current days. The Sun will have destroyed the arrangement long before that happens. The Moon, being smaller, lost this argument long ago - it is already locked to us, which is why there is a far side nobody saw until 1959.