Inquisition's Requisition is one of the optional actions connected with this faction. Personally, I recommend against ignoring them because they are one of the more enjoyable ways of gaining Power points and Influence points. The entire mechanism hinges on supplying the Inquisition with the required materials and resources, thanks to which you contribute to, e.g. equipping the Inquisition's soldiers with better gear.
Each time, you need to start by locating the quartermaster. In the case of the current Inquisition HQ, he is staying in a predetermined spot. As for the rest of the locations, you can find a quartermaster in each encampment, a smaller stronghold and a keep.
Once you meet with the quartermaster, you can interact with the Table of Requisitions (Inspect Requisitions) and learn which materials, resources and other ingredients are required for you to complete the current commission. You can then set out to find these materials. Once you have found everything that you need, you can return to the Table and complete the entire process.
Note! In various main locations of the world, you complete a variety tasks. Once you unlock a given area for the first time, you can meet with one of the quartermasters there, thanks to which you gain access to a new task. Completing a task in a given location does not do the job, because you can unlock more tasks and start looking for more ingredients. Since the tasks connected with Inquisition's Requisitions display in the log and are perceived as quests, they have been described in the walkthrough for the game.