Soul Gems can be found in mimic chests, monster drops, and shops.  These gems can enchant your armors and weapons with increased stats such as resistances and other effects.  Some also add additional skills to your arsenal such as Counter Attacks and automatically activating when hit.  These enchantments open up to you to use with 25 points into Spirituality, and upgrades to be able to use the Legendary rare soul gems with 50 points.  Leveling up your base experience grants the user access to more powerful soul gems.  

Soul Gems can be socketed into both weapons and armors with empty slots.  Weapons max out with the ability to equip up to two soul gems in a one handed weapon and up to four soul gems on a two handed weapon.  Furthermore, your chest armor, footwear, helm and accessory each can hold one soul gem each.