These are items that cannot be equipped or used, but are stored in your inventory because they are needed to advance in the game.
You will get the Kokiri's Emerald automatically when you beat the Deku Tree dungeon. It is one of the three Spiritual Stones needed to open the Door of Time inside the Temple of Time.
You will get the Goron's Ruby automatically from Darunia when you beat the Dodongo's Cavern dungeon. It is the second of three Spiritual Stones needed to open the Door of Time.
You will get the Zora's Sapphire automatically from Princess Ruto when you beat the Inside Jabu-Jabu's Belly dungeon. It is the third and last of the three Spiritual Stones needed to open the Door of Time.
After you pull the Master Sword from the Temple of Time, you will automatically end up in the Light Temple with Rauru the Sage. At the end of the cutscene, he will give you the Light Medallion. This is the first of the six medallions needed to build the rainbow bridge to Ganon's Castle.
After you beat the Forest Temple, you'll automatically transport back to the Chamber of the Sages. Saria will awaken as a Sage and give you the Forest Medallion.
Clear the Fire Temple to be transported back to the Chamber of Sages, where Darunia will give you the Fire Medallion.
Complete the Water Temple and you'll once again return to the Chamber of Sages. Princess Ruto will awaken as a sage and give you the Water Medallion.
After you've dusted off the Shadow Temple, Impa will become a sage and bestow upon you the Shadow Medallion.
Once the Spirit Temple is complete, you'll warp back to the Chamber of Sages for one final time, and Nabooru will give you the Spirit Medallion.