What does the green & blue track halos in Potlatch mean?

As Ed says, the colouring is due to the type of route relations involved. There's a simpler example of something similar (with only two relations involved) here. The blue line is a "route=hiking" relation; the green ones are either just a "route=foot" relation or (in the south of the view) both relations running along the same path.

In your example, to see the relations involved, click on the green line. In the bottom left you can choose "simple" or "advanced" - click "advanced". You'll now see 4 relations - one "route=foot", and 3 "route=hiking". If you double-click on the top one of these an "edit relation" box appears - the name is "Jakobs-Pilgerweg Marburg-Köln". Again in this window you can click "simple" or "advanced" (and also "members"). If you click "advanced" you can see the tags associated with the relation.

There's more information about relations here (Deutsch). They're a way of applying tags together to a group of things that together make up one big thing. Obviously you need to be careful editing things that are part of relations - the E1 relation in your example is part of a route that runs from Italy to Sweden, so local changes can have global consequences.

You can view route relations in OSM like this, and there are other sites (dedicated to hiking) that render them too, like this one.

I believe that the different highlighting is to show that the ways are in certain types of relation. I'm not entirely sure what the green one is, but the blue I think is a relation of type=route. If you click on the way and switch to advanced view you will be able to see which relations a way is in.