A theme is the entire color and design scheme of the board and background you're playing on. There are 9 themes. In order to not explain things backwards:
When you create a path, a pink bonus droplitz is created. These will fall from the dropper at the top of the path.
When all bonus droplitz are collected, the dails involved in the path(s) are destroyed and new ones fall into place.
Every 5 times a path set is destroyed, you will progress to the next theme.
This is easily done in classic mode by making only one or two paths, one from each dropper, and not trying to involve other dials to make more paths. Let the pink droplitz fall into the collectors and then work on the next path. This is the opposite as going for a high score.