What is the particle trail for in Genshin Impact?

The trail is indeed a "current objective" tracker that is displayed for most quests that have a clear objective (so, nothing like "Search this generic area" for example).

What may have tricked you is that the trail only appears when you enable navigation for the current active quest. Sometime it activates by default when you get a new quest, sometime it doesn't (probably it is based on quest priority, Archeon quests seems to get automatic navigation most of the time). It is also worth noticing that it seems there are three possible "navigation experience":

• sparkling path.
• map pin but no path, usually seen for targets outside the city
• generic area (usually an orange circle on the map)

Also notice that distance apparently seems something that is taken in account when the game decides if it should display the sparkling path (I don't think you can get a path for an objective in Liyue if you are standing on Mondstadt bridge for example).

Anyway, I would not worry about this feature. Just remember that if it becomes an annoyance, you can disable it by going to the quest menu and selecting the "cancel navigation" option. This could be useful for taking screenshot since the trail does not disappear in photo mode otherwise....

I only remember seeing it in Mondstadt. I don't remember it leading me to Paimon, but outside is bright, so maybe?

But the video series about not progressing the main quest, which needs you to go to Paimon, clearly shows that the game does not give a path back to Paimon in case you get lost, so...

Yes, from Mondstadt only, this trail appears. Not sure of the trigger conditions, though.