Trails are a neat visual addition to various powers.
You have to define them in assets/<namespace>/palladium/trails/<trail_id>.json. You can find info for all the trails types in the trails.html file in your mods/documentation/palladium folder.

A simple lightning trail could look like this:

{
  "type": "palladium:lightning",
  "spacing": 1,
  "lifetime": 20,
  "glow_color": "#ff0000",
  "amount": 7,
  "thickness": 0.05
}

Then you can reference the trail in a palladium:trail ability like here:

"red_lightning": {
  "type": "palladium:trail",
  "trail": "test:red_lightning_test"
}

You can find examples for some trails in the test pack here.

They are used in this power.