Having established the original method by which humans came to understand how the appearance of a star defined the Earth's orbital position around the Sun and the number of times it turns within the confines of that orbital circuit using an extra day and rotation over a 4 year period and 4 orbital circuits, the use of the average day and modern timekeeping comes into view. No better person than the great John Harrison to explain the principles -

"The application of a Timekeeper to this discovery is founded upon the
following principles: the earth's surface is divided into 360 equal parts (by imaginary lines drawn from North to South) which are called Degrees of Longitude; and its daily revolution Eastward round its own axis is performed in 24 hours; consequently in that period, each of those imaginary lines or degrees, becomes successively opposite to the Sun (which makes the noon or precise middle of the day at each of those degrees and it must follow, that from the time any one of those lines passes the Sun, till the next passes, must be just four minutes, for 24 hours being divided by 360 will give that quantity; so that for every degree of Longitude we sail Westward, it will be noon with us four minutes the later, and for every degree Eastward four minutes the sooner, and so on in proportion for any greater or less quantity. Now, the exact time of the day at the place where we are, can be ascertained by well known and easy observations of the Sun if visible for a few minutes at any time from his being ten degrees high until within an hour of noon, or from an hour after noon until he is only 10 degrees high in the afternoon; if therefore, at any time when such observation is made, a Timekeeper tells us at the same moment what o'clock it is at the place we sailed from, our Longitude is
clearly discovered." John Harrison

So here we have the 24 hour day linked to the passage of the Sun across the meridian each day where one rotation and one day always keep in step and especially February 29th which represents the older astronomical achievement that pins the Earth to its orbital position.

The next explanation is intricate but if readers can follow the principles so far that anchor the 24 hour day to rotation there is little that can go wrong understanding the next step which ties the Lat/Long system to the 24 hour AM/PM system.