You can use these items to upgrade existing weapons go to the armorer in Gran Soren and you'll see an option so upgrade your equipment. I'm pretty sure that you can use the items in storage as well for this which is goddamn genius and I love Capcom for not making me run back and forth needlessly.
Also other than using those items to enhance your weapons and armor you can straight up combine them to make new things. I think its when you're at the inn when you deposit them there is the option to combine. --- So say we all