If you purchase an item from the shop, you may hold on to it and it will have no effect until you declare that you are activating it. Once activated, the item's effect lasts for the remainder of the stage. The activated item is then lost after that stage.
All inventories are also cleared at the end of stage 6, so if you're still holding on to any shop items at that point, you'll need to activate them then (or lose them).
Thanks for explaining, I was a bit confused on that.