The primary (red) map pin is the location for which TPE calculates sun, moon and star data. The lines shown on the map emerging from the primary pin are lines of azimuth, i.e. direction. You can read more about exactly how azimuth is defined here.
The color legend for the thicker lines is built into the timeline itself: you can see in the shot below that moonset and sunrise are shown using lines of the same color as that used in the corresponding timeline entry. The direction of sun and moon are shown using the thinner blue and orange lines:
Shadow and projection lines
As you adjust the selected time of day by scrolling the sun/moon altitude chart left or right, some additional lines are shown.
The very thin orange and blue lines show the projection of sunlight and moonlight for the red pin location. Why would you care? Well, if you were stood at the red pin shooting with the sun or moon to your back, the line indicates the direction the light would fall (i.e. it's the direction the light shines towards, rather than the direction it comes from).
The thick lines in dark brown or dark blue show an indication of shadow length cast by the sun and moon (a bright moon casts shadows at night). In the screenshot below, the sun is much lower in the sky than the moon (+7.7° vs +44.2°), so the sun shadow line is longer. (Of course, you'd only see a moon shadow at night after twilight ends.)
The +6° Shadow Circle
You may be wondering, (i) what does the circle indicate and (ii) how is the shadow length determined.
Assuming flat terrain, shadow length depends on the angle of the light and the height of the object casting the shadow. You can enter a height for the object on the Shadows tab (shown in the screenshot above at the bottom right). When a primary object height has been specified (primary here means the height of an object at the primary pin location, i.e. the red pin), the shadow length is calculated accordingly.
If no primary object height is specified, the app calculates a notional object height such that if the sun or moon were at 6° altitude above the horizon, the tip of the shadow would meet the circle on the map. (The size of the circle is chosen to fit the available screen space).
Once the sun descends below +6°, the shadow line will extend beyond the circle. The app treats this as so-called "Golden Hour" (although we're not huge fans of that term), and the circle is drawn as orange: