This is much simpler then it looks, I will try to explain it in more details.
So we view that the Earth circles the Sun in one year(month branches).
That suggests that in relation to the Earth, the Sun is in specific position. We divide that circle to 360 degrees and we view where the Sun is.
Here is how it looks during the year at the 4 major points of the movement.

The 2 horizontal places of the Earth where it says Summer and Winter are what we call Solstices.
This is the time when the Day ir longest(for Summer), or Day is shortest(Winter).
This are the middle of Wu horse branch and the middle of Zi Rat branch.
That means that if we check when the Solstice is, we can know the precise middle of one branch(as its the end of the first Solar Term that makes the branch and the start of the second)
Where does the longitude come in here?
Well, the longitude or "apparent ecliptical longitude of the Sun)" is just a way to say where on this circle the Sun is.
Apparent means this is when its looked from the Earth(as of course, looking from the Sun, the Earth will be moving, not the Sun).
Ecliptical means that this is in the movement of the ecliptic(that is what is called the plane where this movement is taking place).
Longitude means the position the Sun has, in relation to the movement of the Image.
Sun is the Sun, our local Star.
How we use that... Lets say its 21 june and the Suns longitude is 90.1, now we already know the Sun has just passed the point of its position on the left image in relation to the Earth. So now its still middle of Wu horse branch, but now we just stepped to the second Solar Term(second half) that makes it.
Also means if we know the relation of Day to Night in 2 conservative days we can say what branch we currently are at. While at the Solstices we can even do it with 1 day alone.
In that sense, if we know the longitude, we know where we are in the year in position of the Sun. With 4 major points of Equinoxes and Solstices that mark the 4 major points, the shortest and longest day and the times when the day is equal to the night(on the top and bottom Image).
The other stuff is much simpler, though, this is simple as well, only the terminology make it seem like its not.
Let me know if you need some detail on this. its very simple idea, its just Light that falls on the Earth during the year and the steps through with that happens. Zi Rat being the shortest day, Wu horse being the longest day, so first in the Winter, second in Summer.
(then Mao and You as the day equal to the night in the middle of the movement, while light is increasing in Wood, while light decreasing in Metal).