The Jägertroth is the Jägermonster's set of fundamental duties (or perhaps beliefs), linked inextricably with their loyalty to House Heterodyne. We know this loyalty entails (or at least implies) obedience to the Heterodynes, keeping Heterodyne secrets from outsiders, and not giving up looking for a new Heterodyne, even when there isn't really any hope.
"Troth" is an old word for "oath," and is sworn by all followers of the Heterodyne. Only after an extended period of service did the Heterodynes offer their subjects the Jägerbräu, demanding trustworthiness to the point that they considered
Notably, Captain Vole renounced the Jägertroth and was then for perhaps the only act that the Jägerkin would find unforgivable - , saying they were "weak".
One major significance of this concept is that it underlines the nature of the bond between the Jägerkin and the Heterodynes. The loyalty that Jägers feel for the Heterodynes is not the unthinking command we see with revenants — Jägers have been known to talk back to Heterodynes if they feel something is important, they’ve been able to make bargains with the Baron Wulfenbach without Heterodyne approval, the Generals have been pursuing their own agenda regarding Da Boyz and the Heterodyne heir, and Jägers were even shown to be happy that Euphrosynia Heterodyne was being married to Ogglespoon against her will. If anything, the link between Jäger and Heterodyne seems more to be a lord-vassal relationship than the standard master-construct relationship.