Every SHQ, zone and unit has its own inventory. You can check the inventory of the zone of the currently selected hex in the Items tab of the bottom panel, and the selected unit's inventory in one of the subtabs of the unit tab.
During logistics resolution, zones and units request resources and replacements they need, their SHQ ships those resources to them (within the bounds of available logistical capacity), and then zones produce resources and ask their SHQ to pick up any excess beyond a small local stockpile (again, subject to available logistical capacity - if lacking, this will generate a backlog of resources in the zone inventory). Any points left over from this process can be used to perform manual logistics operations during your turn, like strategic movement and unit equipment upgrades.
You can check the logistics points required to move most things in section 220.127.116.11 of the manual. There are some statistics regarding logistics available under Stats in the top right, and with a SHQ selected, one of the bottom panel unit tab sub-tabs lists how many logistics points' worth of shipping was requested from the SHQ and how much of that it managed to fulfill. The right-side panel has view modes that allow you to inspect details about your logistical network, like where your bottlenecks are, how many logistical points reached a given hex and how many are left after everything that was shipped. You can also use the traffic lights order mode to get further micro-detail on what your logistics network is doing and make micro-adjustments to it, but that starts to get pretty obtuse.
You should always try to avoid bottlenecks and have some spare logistics points available on all your logistical routes, or your logistics network is likely to have difficulties. Until you are much more familiar with the logistics system, if there are bottlenecks, your first resort should always be to upgrade your truck depots or rail stations in nearby zones. Up-to-date versions of the game will automatically distribute your logistical points in a fashion which is usually serviceable, though often not the most optimal possible.
< Message edited by Soar_Slitherine -- 8/26/2020 3:15:19 PM >