Apologies for the late response.
"Any Action or Reaction granted by an EUSOCIAL system can be activated by an adjacent allied character, as long as you allow them to do so. Eusocial weapons can be used to Skirmish or Barrage by adjacent allies as if they had them installed. The owner spends charges and takes heat generated by the system or weapon as normal, while the user provides its own talents, traits, core bonuses and other modifiers for the instance of use." (Page 34)
Essentially the Eusocial tag allows adjacent characters to use a weapon or system you have installed as if they had it installed; there are some clarifications we want to make in the next update about how that interacts with systems that possess Limited Charges or Systems that can be "charged" (such as stasis bolt).It is, admittedly, a bit confusing in terms of the sheer amount of edge cases that exist, and this has not been designed with other homebrew content in mind, nor content packs such as Dustgrave (it is, at least, fully compatible with all of the First-Party content not written by non-Massif staff).
I hope that helps.