Go back to the first Conquest page, where you select which Sector you want to enter. On the right side of the screen there is a small button labeled "Inventory." Click that, which brings up two tabs: left tab "Data Disks", right tab "Consumables." Click on Consumables.
Now there are three sections: Boosters, Medpacs, Techs. Click each of these to see the items you have collected. Click an item to use it; it will give you the option to Confirm before the item is consumed. From there, we guess that the item actually works in the battles. I assume the descriptor "Max Duration" means that it will last for X number of battles, but cannot say for sure.